Primality by trial division: Difference between revisions
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{{task|Prime Numbers}}
;Task:
Write a boolean function that tells whether a given integer is prime.
Remember that '''1''' and all non-positive numbers are not prime.
Use trial division.
Even numbers greater than '''2''' may be eliminated right away.
A loop from '''3''' to '''√{{overline| n }} ''' will suffice, but other loops are allowed.
;Related tasks:
* [[count in factors]]
* [[prime decomposition]]
* [[AKS test for primes]]
* [[factors of an integer]]
* [[Sieve of Eratosthenes]]
* [[factors of a Mersenne number]]
* [[trial factoring of a Mersenne number]]
* [[partition an integer X into N primes]]
* [[sequence of primes by Trial Division]]
<br><br>
=={{header|11l}}==
<syntaxhighlight lang="11l">F is_prime(n)
I n < 2
R 0B
L(i) 2..Int(sqrt(n))
I n % i == 0
R 0B
R 1B</syntaxhighlight>
=={{header|360 Assembly}}==
<syntaxhighlight lang="360asm">* Primality by trial division 26/03/2017
PRIMEDIV CSECT
USING PRIMEDIV,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R10,PG pgi=0
LA R6,1 i=1
DO WHILE=(C,R6,LE,=F'50') do i=1 to 50
LR R1,R6 i
BAL R14,ISPRIME call isprime(i)
IF C,R0,EQ,=F'1' THEN if isprime(i) then
XDECO R6,XDEC edit i
MVC 0(4,R10),XDEC+8 output i
LA R10,4(R10) pgi+=4
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
*------- ---- ----------------------------------------
ISPRIME EQU * function isprime(n)
IF C,R1,LE,=F'1' THEN if n<=1 then
LA R0,0 return(0)
BR R14 return
ENDIF , endif
IF C,R1,EQ,=F'2' THEN if n=2 then
LA R0,1 return(1)
BR R14 return
ENDIF , endif
LR R4,R1 n
N R4,=X'00000001' n and 1
IF LTR,R4,Z,R4 THEN if mod(n,2)=0 then
LA R0,0 return(0)
BR R14 return
ENDIF , endif
LA R7,3 j=3
LA R5,9 r5=j*j
DO WHILE=(CR,R5,LE,R1) do j=3 by 2 while j*j<=n
LR R4,R1 n
SRDA R4,32 ~
DR R4,R7 /j
IF LTR,R4,Z,R4 THEN if mod(n,j)=0 then
LA R0,0 return(0)
BR R14 return
ENDIF , endif
LA R7,2(R7) j+=2
LR R5,R7 j
MR R4,R7 r5=j*j
ENDDO , enddo j
LA R0,1 return(1)
BR R14 return
*------- ---- ----------------------------------------
PG DC CL80' ' buffer
XDEC DS CL12 temp for xdeco
YREGS
END PRIMEDIV</syntaxhighlight>
{{out}}
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
=={{header|68000 Assembly}}==
<syntaxhighlight lang="68000devpac">isPrime:
; REG USAGE:
; D0 = input (unsigned 32-bit integer)
; D1 = temp storage for D0
; D2 = candidates for possible factors
; D3 = temp storage for quotient/remainder
; D4 = total count of proper divisors.
MOVEM.L D1-D4,-(SP) ;push data regs except D0
MOVE.L #0,D1
MOVEM.L D1,D2-D4 ;clear regs D1 thru D4
CMP.L #0,D0
BEQ notPrime
CMP.L #1,D0
BEQ notPrime
CMP.L #2,D0
BEQ wasPrime
MOVE.L D0,D1 ;D1 will be used for temp storage.
AND.L #1,D1 ;is D1 even?
BEQ notPrime ;if so, it's not prime!
MOVE.L D0,D1 ;restore D1
MOVE.L #3,D2 ;start with 3
computeFactors:
DIVU D2,D1 ;remainder is in top 2 bytes, quotient in bottom 2.
MOVE.L D1,D3 ;temporarily store into D3 to check the remainder
SWAP D3 ;swap the high and low words of D3. Now bottom 2 bytes contain remainder.
CMP.W #0,D3 ;is the bottom word equal to 0?
BNE D2_Wasnt_A_Divisor ;if not, D2 was not a factor of D1.
ADDQ.L #1,D4 ;increment the count of proper divisors.
CMP.L #2,D4 ;is D4 two or greater?
BCC notPrime ;if so, it's not prime! (Ends early. We'll need to check again if we made it to the end.)
D2_Wasnt_A_Divisor:
MOVE.L D0,D1 ;restore D1.
ADDQ.L #1,D2 ;increment D2
CMP.L D2,D1 ;is D2 now greater than D1?
BLS computeFactors ;if not, loop again
CMP.L #1,D4 ;was there only one factor?
BEQ wasPrime ;if so, D0 was prime.
notPrime:
MOVE.L #0,D0 ;return false
MOVEM.L (SP)+,D1-D4 ;pop D1-D4
RTS
wasPrime:
MOVE.L #1,D0 ;return true
MOVEM.L (SP)+,D1-D4 ;pop D1-D4
RTS
;end of program</syntaxhighlight>
=={{header|AArch64 Assembly}}==
{{works with|as|Raspberry Pi 3B version Buster 64 bits}}
<syntaxhighlight lang="aarch64 assembly">
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program testPrime64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessStartPgm: .asciz "Program start \n"
szMessEndPgm: .asciz "Program normal end.\n"
szMessNotPrime: .asciz "Not prime.\n"
szMessPrime: .asciz "Prime\n"
szCarriageReturn: .asciz "\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
.align 4
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main: // program start
ldr x0,qAdrszMessStartPgm // display start message
bl affichageMess
ldr x0,qVal
bl isPrime // test prime ?
cmp x0,#0
beq 1f
ldr x0,qAdrszMessPrime // yes
bl affichageMess
b 2f
1:
ldr x0,qAdrszMessNotPrime // no
bl affichageMess
2:
ldr x0,qAdrszMessEndPgm // display end message
bl affichageMess
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform system call
qAdrszMessStartPgm: .quad szMessStartPgm
qAdrszMessEndPgm: .quad szMessEndPgm
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrszMessNotPrime: .quad szMessNotPrime
qAdrszMessPrime: .quad szMessPrime
//qVal: .quad 1042441 // test not prime
//qVal: .quad 1046527 // test prime
//qVal: .quad 37811 // test prime
//qVal: .quad 1429671721 // test not prime (37811 * 37811)
qVal: .quad 100000004437 // test prime
/******************************************************************/
/* test if number is prime */
/******************************************************************/
/* x0 contains the number */
/* x0 return 1 if prime else return 0 */
isPrime:
stp x1,lr,[sp,-16]! // save registers
cmp x0,1 // <= 1 ?
ble 98f
cmp x0,3 // 2 and 3 prime
ble 97f
tst x0,1 // even ?
beq 98f
mov x11,3 // first divisor
1:
udiv x12,x0,x11
msub x13,x12,x11,x0 // compute remainder
cbz x13,98f // end if zero
add x11,x11,#2 // increment divisor
cmp x11,x12 // divisors<=quotient ?
ble 1b // loop
97:
mov x0,1 // return prime
b 100f
98:
mov x0,0 // not prime
b 100f
100:
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
</syntaxhighlight>
=={{header|ABAP}}==
<
public
create public .
Line 108 ⟶ 367:
RETURN.
endmethod.
ENDCLASS.</
=={{header|ABC}}==
<syntaxhighlight lang="ABC">HOW TO REPORT prime n:
REPORT n>=2 AND NO d IN {2..floor root n} HAS n mod d = 0
FOR n IN {1..100}:
IF prime n: WRITE n</syntaxhighlight>
{{out}}
<pre>2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</pre>
=={{header|ACL2}}==
<
(declare (xargs :measure (nfix (- x i))))
(if (zp (- (- x i) 1))
Line 120 ⟶ 388:
(defun is-prime (x)
(or (= x 2)
(is-prime-r x 2)))</
=={{header|Action!}}==
<syntaxhighlight lang="action!">BYTE FUNC IsPrime(CARD a)
CARD i
IF a<=1 THEN
RETURN (0)
FI
FOR i=2 TO a/2
DO
IF a MOD i=0 THEN
RETURN (0)
FI
OD
RETURN (1)
PROC Test(CARD a)
IF IsPrime(a) THEN
PrintF("%I is prime%E",a)
ELSE
PrintF("%I is not prime%E",a)
FI
RETURN
PROC Main()
Test(13)
Test(997)
Test(1)
Test(6)
Test(120)
Test(0)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Primality_by_trial_division.png Screenshot from Atari 8-bit computer]
<pre>
13 is prime
997 is prime
1 is not prime
6 is not prime
120 is not prime
0 is not prime
</pre>
=={{header|ActionScript}}==
<
{
if(n < 2) return false;
Line 131 ⟶ 442:
if(n % i == 0) return false;
return true;
}</
=={{header|Ada}}==
<
Test : Natural;
begin
if Item
elsif Item = 2 then
return True;
elsif Item mod 2 = 0 then
return False;
else
Test := 3;
while Test <= Integer(Sqrt(Float(Item))) loop
if Item mod Test = 0 then
end if;
Test := Test + 2;
end loop;
end if;
return
end Is_Prime;</
<code>Sqrt</code> is made visible by a with / use clause on <code>Ada.Numerics.Elementary_Functions</code>.
With Ada 2012, the function can be made more compact as an expression function (but without loop optimized by skipping even numbers) :
<syntaxhighlight lang="ada">function Is_Prime(Item : Positive) return Boolean is
(Item /= 1 and then
(for all Test in 2..Integer(Sqrt(Float(Item))) => Item mod Test /= 0));</syntaxhighlight>
As an alternative, one can use the generic function Prime_Numbers.Is_Prime, as specified in [[Prime decomposition#Ada]], which also implements trial division.
<syntaxhighlight lang="ada">with Prime_Numbers;
procedure Test_Prime is
package Integer_Numbers is new
Prime_Numbers (Natural, 0, 1, 2);
use Integer_Numbers;
begin
if Is_Prime(12) or (not Is_Prime(13)) then
raise Program_Error with "Test_Prime failed!";
end if;
end Test_Prime;</syntaxhighlight>
=={{header|ALGOL 60}}==
{{works with|A60}}
<syntaxhighlight lang = "algol">
begin
boolean procedure isprime(n);
value n; integer n;
begin
comment - local procedure tests whether n is even;
boolean procedure even(n);
value n; integer n;
even := entier(n / 2) * 2 = n;
if n < 2 then
isprime := false
else if even(n) then
isprime := (n = 2)
else
begin
comment - check odd divisors up to sqrt(n);
integer i, limit;
boolean divisible;
i := 3;
limit := entier(sqrt(n));
divisible := false;
for i := i while i <= limit and not divisible do
begin
if entier(n / i) * i = n then
divisible := true;
i := i + 2
end;
isprime := if divisible then false else true;
end;
end;
comment - exercise the procedure;
integer i;
outstring(1,"Testing first 50 numbers for primality:\n");
for i := 1 step 1 until 50 do
if isprime(i) then
outinteger(1,i);
end
</syntaxhighlight>
{{out}}
<pre>
Testing first 50 numbers for primality:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
</pre>
=={{header|ALGOL 68}}==
Line 158 ⟶ 543:
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}}
{{prelude/is_prime.a68}};
<
INT upb=100;
printf(($" The primes up to "g(-3)" are:"l$,upb));
Line 167 ⟶ 552:
OD;
printf($l$)
)</
{{out}}
The primes up to 100 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
=={{header|ALGOL-M}}==
<syntaxhighlight lang="algol">
BEGIN
% RETURN P MOD Q %
INTEGER FUNCTION MOD(P, Q);
INTEGER P, Q;
BEGIN
MOD := P - Q * (P / Q);
END;
% RETURN INTEGER SQUARE ROOT OF N %
INTEGER FUNCTION ISQRT(N);
INTEGER N;
BEGIN
INTEGER R1, R2;
R1 := N;
R2 := 1;
WHILE R1 > R2 DO
BEGIN
R1 := (R1+R2) / 2;
R2 := N / R1;
END;
ISQRT := R1;
END;
% RETURN 1 IF N IS PRIME, OTHERWISE 0 %
INTEGER FUNCTION ISPRIME(N);
INTEGER N;
BEGIN
IF N = 2 THEN
ISPRIME := 1
ELSE IF (N < 2) OR (MOD(N,2) = 0) THEN
ISPRIME := 0
ELSE % TEST ODD NUMBERS UP TO SQRT OF N %
BEGIN
INTEGER I, LIMIT;
LIMIT := ISQRT(N);
I := 3;
WHILE I <= LIMIT AND MOD(N,I) <> 0 DO
I := I + 2;
ISPRIME := (IF I <= LIMIT THEN 0 ELSE 1);
END;
END;
% TEST FOR PRIMES IN RANGE 1 TO 50 %
INTEGER I;
WRITE("");
FOR I := 1 STEP 1 UNTIL 50 DO
BEGIN
IF ISPRIME(I)=1 THEN WRITEON(I," "); % WORKS FOR 80 COL SCREEN %
END;
END
</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29
31 37 41 43 47
</pre>
=={{
<syntaxhighlight lang="algolw">% returns true if n is prime, false otherwise %
% uses trial division %
logical procedure isPrime ( integer value n ) ;
if n < 3 or not odd( n ) then n = 2
else begin
% odd number > 2 %
integer f, rootN;
logical havePrime;
f := 3;
rootN := entier( sqrt( n ) );
havePrime := true;
while f <= rootN and havePrime do begin
havePrime := ( n rem f ) not = 0;
f := f + 2
end;
havePrime
end isPrime ;</syntaxhighlight>
Test program:
<syntaxhighlight lang="algolw">begin
logical procedure isPrime ( integer value n ) ; algol "isPrime" ;
for i := 0 until 32 do if isPrime( i ) then writeon( i_w := 1,s_w := 1, i )
end.</syntaxhighlight>
{{out}}
2 3 5 7 11 13 17 19 23 29 31
=={{header|APL}}==
<syntaxhighlight lang="APL">prime ← 2=0+.=⍳|⊣</syntaxhighlight>
{{out}}
<syntaxhighlight lang="APL"> (⊢(/⍨)prime¨)⍳100
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</syntaxhighlight>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">on isPrime(n)
if (n < 3) then return (n is 2)
if (n mod 2 is 0) then return false
repeat with i from 3 to (n ^ 0.5) div 1 by 2
if (n mod i is 0) then return false
end repeat
return true
end isPrime
-- Test code:
set output to {}
repeat with n from -7 to 100
if (isPrime(n)) then set end of output to n
end repeat
return output</syntaxhighlight>
Or eliminating multiples of 3 at the start as well as those of 2:
<syntaxhighlight lang="applescript">on isPrime(n)
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
repeat with i from 5 to (n ^ 0.5) div 1 by 6
if ((n mod i is 0) or (n mod (i + 2) is 0)) then return false
end repeat
return true
end isPrime
-- Test code:
set output to {}
repeat with n from -7 to 100
if (isPrime(n)) then set end of output to n
end repeat
return output</syntaxhighlight>
{{output}}
<syntaxhighlight lang="applescript">{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}</syntaxhighlight>
=={{header|ARM Assembly}}==
{{works with|as|Raspberry Pi <br> or android 32 bits with application Termux}}
<syntaxhighlight lang ARM Assembly>
/* ARM assembly Raspberry PI */
/* program testtrialprime.s */
/************************************/
/* Constantes */
/************************************/
/* for this file see task include a file in language ARM assembly*/
.include "../constantes.inc"
//.include "../../ficmacros32.inc" @ for debugging developper
/************************************/
/* Initialized data */
/************************************/
.data
szMessPrime: .asciz " is prime.\n"
szMessNotPrime: .asciz " is not prime.\n"
szCarriageReturn: .asciz "\n"
szMessStart: .asciz "Program 32 bits start.\n"
/************************************/
/* UnInitialized data */
/************************************/
.bss
sZoneConv: .skip 24
/************************************/
/* code section */
/************************************/
.text
.global main
main: @ entry of program
ldr r0,iAdrszMessStart
bl affichageMess
mov r0,#19
bl testPrime
ldr r0,iStart @ number
bl testPrime
ldr r0,iStart1 @ number
bl testPrime
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
swi 0 @ perform the system call
iAdrsZoneConv: .int sZoneConv
iAdrszMessPrime: .int szMessPrime
iAdrszMessNotPrime: .int szMessNotPrime
iAdrszCarriageReturn: .int szCarriageReturn
iAdrszMessStart: .int szMessStart
iStart: .int 2600002183
iStart1: .int 4124163031
/******************************************************************/
/* test if number is prime */
/******************************************************************/
/* r0 contains the number */
testPrime:
push {r1,r2,lr} @ save registers
mov r2,r0
ldr r1,iAdrsZoneConv
bl conversion10 @ decimal conversion
ldr r0,iAdrsZoneConv
bl affichageMess
mov r0,r2
bl isPrime
cmp r0,#0
beq 1f
ldr r0,iAdrszMessPrime
bl affichageMess
b 100f
1:
ldr r0,iAdrszMessNotPrime
bl affichageMess
100:
pop {r1,r2,pc} @ restaur registers
/******************************************************************/
/* test if number is prime */
/******************************************************************/
/* r0 contains the number */
/* r0 return 1 if prime else return 0 */
isPrime:
push {r4,lr} @ save registers
cmp r0,#1 @ <= 1 ?
movls r0,#0 @ not prime
bls 100f
cmp r0,#3 @ 2 and 3 prime
movls r0,#1
bls 100f
tst r0,#1 @ even ?
moveq r0,#0 @ not prime
beq 100f
mov r4,r0 @ save number
mov r1,#3 @ first divisor
1:
mov r0,r4 @ number
bl division
add r1,r1,#2 @ increment divisor
cmp r3,#0 @ remainder = zero ?
moveq r0,#0 @ not prime
beq 100f
cmp r1,r2 @ divisors<=quotient ?
ble 1b @ loop
mov r0,#1 @ return prime
100:
pop {r4,pc} @ restaur registers
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
/* for this file see task include a file in language ARM assembly*/
.include "../affichage.inc"
</syntaxhighlight>
{{Out}}
<pre>
Program 32 bits start.
19 is prime.
2600002183 is prime.
4124163031 is not prime.
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">isPrime?: function [n][
if n=2 -> return true
if n=3 -> return true
if or? n=<1 0=n%2 -> return false
high: to :integer sqrt n
loop high..2 .step: 3 'i [
if 0=n%i -> return false
]
return true
]
loop 1..20 'i [
print ["isPrime?" i "=" isPrime? i ]
]</syntaxhighlight>
{{out}}
<pre>isPrime? 1 = false
isPrime? 2 = true
isPrime? 3 = true
isPrime? 4 = false
isPrime? 5 = true
isPrime? 6 = false
isPrime? 7 = true
isPrime? 8 = false
isPrime? 9 = false
isPrime? 10 = false
isPrime? 11 = true
isPrime? 12 = false
isPrime? 13 = true
isPrime? 14 = false
isPrime? 15 = false
isPrime? 16 = false
isPrime? 17 = true
isPrime? 18 = false
isPrime? 19 = true
isPrime? 20 = false</pre>
=={{header|AutoHotkey}}==
[http://www.autohotkey.com/forum/topic44657.html Discussion]
<
Loop
MsgBox % A_Index-3 . " is " . (IsPrime(A_Index-3) ? "" : "not ") . "prime."
Line 183 ⟶ 863:
d := k+(k<7 ? 1+(k>2) : SubStr("6-----4---2-4---2-4---6-----2",Mod(k,30),1))
Return n < 3 ? n>1 : Mod(n,k) ? (d*d <= n ? IsPrime(n,d) : 1) : 0
}</
=={{
<syntaxhighlight lang="autoit">#cs ----------------------------------------------------------------------------
AutoIt Version: 3.3.8.1
Line 220 ⟶ 899:
Return True
EndFunc
main()</syntaxhighlight>
=={{header|AWK}}==
Line 228 ⟶ 906:
Or more legibly, and with n <= 1 handling
<
if (n <= 1) return 0
for (d = 2; d <= sqrt(n); d++)
Line 235 ⟶ 913:
}
{print prime($1)}</
=={{header|B}}==
==={{header|B as on PDP7/UNIX0}}===
{{trans|C}}
{{works with|B as on PDP7/UNIX0|(proto-B?)}}
<syntaxhighlight lang="b">isprime(n) {
auto p;
if(n<2) return(0);
if(!(n%2)) return(n==2);
p=3;
while(n/p>p) {
if(!(n%p)) return(0);
p=p+2;
}
return(1);
}</syntaxhighlight>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
<syntaxhighlight lang="basic"> 100 DEF FN MOD(NUM) = NUM - INT (NUM / DIV) * DIV: REM NUM MOD DIV
110 FOR I = 1 TO 99
120 V = I: GOSUB 200"ISPRIME
130 IF ISPRIME THEN PRINT " "I;
140 NEXT I
150 END
200 ISPRIME = FALSE: IF V < 2 THEN RETURN
210 DIV = 2:ISPRIME = FN MOD(V): IF NOT ISPRIME THEN ISPRIME = V = 2: RETURN
220 LIMIT = SQR (V): IF LIMIT > = 3 THEN FOR DIV = 3 TO LIMIT STEP 2:ISPRIME = FN MOD(V): IF ISPRIME THEN NEXT DIV
230 RETURN</syntaxhighlight>
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="freebasic">for i = 1 to 99
if isPrime(i) then print string(i); " ";
next i
end
function isPrime(v)
if v < 2 then return False
if v mod 2 = 0 then return v = 2
if v mod 3 = 0 then return v = 3
d = 5
while d * d <= v
if v mod d = 0 then return False else d += 2
end while
return True
end function</syntaxhighlight>
==={{header|BBC BASIC}}===
<syntaxhighlight lang="bbcbasic"> FOR i% = -1 TO 100
IF FNisprime(i%) PRINT ; i% " is prime"
NEXT
END
DEF FNisprime(n%)
IF n% <= 1 THEN = FALSE
IF n% <= 3 THEN = TRUE
IF (n% AND 1) = 0 THEN = FALSE
LOCAL t%
FOR t% = 3 TO SQR(n%) STEP 2
IF n% MOD t% = 0 THEN = FALSE
NEXT
= TRUE</syntaxhighlight>
{{out}}
<pre>2 is prime
3 is prime
5 is prime
7 is prime
11 is prime
13 is prime
17 is prime
19 is prime
23 is prime
29 is prime
31 is prime
37 is prime
41 is prime
43 is prime
47 is prime
53 is prime
59 is prime
61 is prime
67 is prime
71 is prime
73 is prime
79 is prime
83 is prime
89 is prime
97 is prime</pre>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">for i = 1 to 50
if i < 2 then
let p = 0
else
if i = 2 then
let p = 1
else
if i % 2 = 0 then
let p = 0
else
let p = 1
for j = 3 to int(i ^ .5) step 2
if i % j = 0 then
let p = 0
break j
endif
wait
next j
endif
endif
endif
if p <> 0 then
print i
endif
next i</syntaxhighlight>
{{out| Output}}<pre>2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 </pre>
==={{header|FBSL}}===
The second function (included by not used) I would have thought would be faster because it lacks the SQR() function. As it happens, the first is over twice as fast.
<syntaxhighlight lang="qbasic">#APPTYPE CONSOLE
FUNCTION ISPRIME(n AS INTEGER) AS INTEGER
IF n = 2 THEN
RETURN TRUE
ELSEIF n <= 1 ORELSE n MOD 2 = 0 THEN
RETURN FALSE
ELSE
FOR DIM i = 3 TO SQR(n) STEP 2
IF n MOD i = 0 THEN
RETURN FALSE
END IF
NEXT
RETURN TRUE
END IF
END FUNCTION
FUNCTION ISPRIME2(N AS INTEGER) AS INTEGER
IF N <= 1 THEN RETURN FALSE
DIM I AS INTEGER = 2
WHILE I * I <= N
IF N MOD I = 0 THEN
RETURN FALSE
END IF
I = I + 1
WEND
RETURN TRUE
END FUNCTION
' Test and display primes 1 .. 50
DIM n AS INTEGER
FOR n = 1 TO 50
IF ISPRIME(n) THEN
PRINT n, " ";
END IF
NEXT
PAUSE</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Press any key to continue...
</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">' FB 1.05.0 Win64
Function isPrime(n As Integer) As Boolean
If n < 2 Then Return False
If n = 2 Then Return True
If n Mod 2 = 0 Then Return False
Dim limit As Integer = Sqr(n)
For i As Integer = 3 To limit Step 2
If n Mod i = 0 Then Return False
Next
Return True
End Function
' To test this works, print all primes under 100
For i As Integer = 1 To 99
If isPrime(i) Then
Print Str(i); " ";
End If
Next
Print : Print
Print "Press any key to quit"
Sleep</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
</pre>
==={{header|FutureBasic}}===
<syntaxhighlight lang="futurebasic">window 1, @"Primality By Trial Division", (0,0,480,270)
local fn isPrime( n as long ) as Boolean
long i
Boolean result
if n < 2 then result = NO : exit fn
if n = 2 then result = YES : exit fn
if n mod 2 == 0 then result = NO : exit fn
result = YES
for i = 3 to int( n^.5 ) step 2
if n mod i == 0 then result = NO : break
next i
end fn = result
long i, j = 0
print "Prime numbers between 0 and 1000:"
for i = 0 to 1000
if ( fn isPrime(i) != _false )
printf @"%3d\t",i : j++
if j mod 10 == 0 then print
end if
next
HandleEvents</syntaxhighlight>
{{out}}
<pre>
Prime numbers between 0 and 1000:
2 3 5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997
</pre>
==={{header|Gambas}}===
'''[https://gambas-playground.proko.eu/?gist=85fbc7936b17b3009af282752aa29df7 Click this link to run this code]'''
<syntaxhighlight lang="gambas">'Reworked from the BBC Basic example
Public Sub Main()
Dim iNum As Integer
For iNum = 1 To 100
If FNisprime(iNum) Then Print iNum & " is prime"
Next
End
'___________________________________________________
Public Sub FNisprime(iNum As Integer) As Boolean
Dim iLoop As Integer
Dim bReturn As Boolean = True
If iNum <= 1 Then bReturn = False
If iNum <= 3 Then bReturn = True
If (iNum And 1) = 0 Then bReturn = False
For iLoop = 3 To Sqr(iNum) Step 2
If iNum Mod iLoop = 0 Then bReturn = False
Next
Return bReturn
End</syntaxhighlight>
{{out}}
<pre>1 is prime
3 is prime
5 is prime
7 is prime
11 is prime
......
73 is prime
79 is prime
83 is prime
89 is prime
97 is prime</pre>
==={{header|IS-BASIC}}===
<syntaxhighlight lang="is-basic">100 PROGRAM "Prime.bas"
110 FOR X=0 TO 100
120 IF PRIME(X) THEN PRINT X;
130 NEXT
140 DEF PRIME(N)
150 IF N=2 THEN
160 LET PRIME=-1
170 ELSE IF N<=1 OR MOD(N,2)=0 THEN
180 LET PRIME=0
190 ELSE
200 LET PRIME=-1
210 FOR I=3 TO CEIL(SQR(N)) STEP 2
220 IF MOD(N,I)=0 THEN LET PRIME=0:EXIT FOR
230 NEXT
240 END IF
250 END DEF</syntaxhighlight>
==={{header|Liberty BASIC}}===
{{works with|Just BASIC}}
<syntaxhighlight lang="lb">print "Rosetta Code - Primality by trial division"
print
[start]
input "Enter an integer: "; x
if x=0 then print "Program complete.": end
if isPrime(x) then print x; " is prime" else print x; " is not prime"
goto [start]
function isPrime(p)
p=int(abs(p))
if p=2 then isPrime=1: exit function 'prime
if p=0 or p=1 or (p mod 2)=0 then exit function 'not prime
for i=3 to sqr(p) step 2
if (p mod i)=0 then exit function 'not prime
next i
isPrime=1
end function</syntaxhighlight>
{{out}}
<pre>Rosetta Code - Primality by trial division
Enter an integer: 1
1 is not prime
Enter an integer: 2
2 is prime
Enter an integer:
Program complete.</pre>
==={{header|PureBasic}}===
<syntaxhighlight lang="purebasic">Procedure.i IsPrime(n)
Protected k
If n = 2
ProcedureReturn #True
EndIf
If n <= 1 Or n % 2 = 0
ProcedureReturn #False
EndIf
For k = 3 To Int(Sqr(n)) Step 2
If n % k = 0
ProcedureReturn #False
EndIf
Next
ProcedureReturn #True
EndProcedure</syntaxhighlight>
==={{header|QuickBASIC}}===
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
Returns 1 for prime, 0 for non-prime
<syntaxhighlight lang="qbasic">' Primality by trial division
' Test and display primes 1 .. 50
DECLARE FUNCTION prime% (n!)
FOR n = 1 TO 50
IF prime(n) = 1 THEN PRINT n;
NEXT n
FUNCTION prime% (n!)
STATIC i AS INTEGER
IF n = 2 THEN
Line 255 ⟶ 1,318:
NEXT i
END IF
END FUNCTION</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
</pre>
==={{header|Run BASIC}}===
{{works with|Just BASIC}}
<syntaxhighlight lang="runbasic">' Test and display primes 1 .. 50
for i = 1 TO 50
if prime(i) <> 0 then print i;" ";
next i
FUNCTION prime(n)
if n < 2 then prime = 0 : goto [exit]
if n = 2 then prime = 1 : goto [exit]
if n mod 2 = 0 then prime = 0 : goto [exit]
prime = 1
for i = 3 to int(n^.5) step 2
if n mod i = 0 then prime = 0 : goto [exit]
next i
[exit]
END FUNCTION</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47
</pre>
==={{header|S-BASIC}}===
<syntaxhighlight lang="s-basic">
$lines
$constant FALSE = 0
$constant TRUE = 0FFFFH
rem - return p mod q
function mod(p, q = integer) = integer
end = p - q * (p / q)
rem - return true (-1) if n is prime, otherwise false (0)
function isprime(n = integer) = integer
var i, limit, result = integer
if n = 2 then
result = TRUE
else if (n < 2) or (mod(n,2) = 0) then
result = FALSE
else
begin
limit = int(sqr(n))
i = 3
while (i <= limit) and (mod(n, i) <> 0) do
i = i + 2
result = not (i <= limit)
end
end = result
rem - test by looking for primes in range 1 to 50
var i = integer
for i = 1 to 50
if isprime(i) then print using "#####";i;
next i
end
</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
</pre>
==={{header|TI-83 BASIC}}===
Prompt A
If A=2:Then
Disp "PRIME"
Stop
End
If (fPart(A/2)=0 and A>0) or A<2:Then
Disp "NOT PRIME"
Stop
End
1→P
For(B,3,int(√(A)))
If FPart(A/B)=0:Then
0→P
√(A)→B
End
B+1→B
End
If P=1:Then
Disp "PRIME"
Else
Disp "NOT PRIME"
End
==={{header|Tiny BASIC}}===
{{works with|TinyBasic}}
<syntaxhighlight lang="basic">10 REM Primality by trial division
20 PRINT "Enter a number "
30 INPUT P
40 GOSUB 1000
50 IF Z = 1 THEN PRINT "It is prime."
60 IF Z = 0 THEN PRINT "It is not prime."
70 END
990 REM Primality of the number P by trial division
1000 IF P < 2 THEN RETURN
1010 LET Z = 1
1020 IF P < 4 THEN RETURN
1030 LET I = 2
1040 IF (P / I) * I = P THEN LET Z = 0
1050 IF Z = 0 THEN RETURN
1060 LET I = I + 1
1070 IF I * I <= P THEN GOTO 1040
1080 RETURN</syntaxhighlight>
==={{header|True BASIC}}===
{{trans|QuickBASIC}}
<syntaxhighlight lang="qbasic">FUNCTION isPrime (n)
IF n = 2 THEN
LET isPrime = 1
ELSEIF n <= 1 OR REMAINDER(n, 2) = 0 THEN
LET isPrime = 0
ELSE
LET isPrime = 1
FOR i = 3 TO INT(SQR(n)) STEP 2
IF REMAINDER(n, i) = 0 THEN
LET isPrime = 0
EXIT FUNCTION
END IF
NEXT i
END IF
END FUNCTION
FOR n = 1 TO 50
IF
NEXT n
END</syntaxhighlight>
==={{header|uBasic/4tH}}===
<syntaxhighlight lang="text">10 LET n=0: LET p=0
20 INPUT "Enter number: ";n
30 LET p=0 : IF n>1 THEN GOSUB 1000
40 IF p=0 THEN PRINT n;" is not prime!"
50 IF p#0 THEN PRINT n;" is prime!"
60 GOTO 10
1000 REM ***************
1001 REM * PRIME CHECK *
1002 REM ***************
1010 LET p=0
1020 IF (n%2)=0 THEN RETURN
1030 LET p=1 : PUSH n,0 : GOSUB 9030
1040 FOR i=3 TO POP() STEP 2
1050 IF (n%i)=0 THEN LET p=0: PUSH n,0 : GOSUB 9030 : LET i=POP()
1060 NEXT i
1070 RETURN
9030 Push ((10^(Pop()*2))*Pop()) : @(255)=Tos()
9040 Push (@(255) + (Tos()/@(255)))/2
If Abs(@(255)-Tos())<2 Then @(255)=Pop() : If Pop() Then Push @(255) : Return
@(255) = Pop() : Goto 9040
REM ** This is an integer SQR subroutine. Output is scaled by 10^(TOS()).</syntaxhighlight>
==={{header|VBA}}===
<syntaxhighlight lang="vb">Option Explicit
Sub FirstTwentyPrimes()
Dim count As Integer, i As Long, t(19) As String
Do
i = i + 1
If IsPrime(i) Then
t(count) = i
count = count + 1
End If
Loop While count <= UBound(t)
Debug.Print Join(t, ", ")
End Sub
Function IsPrime(Nb As Long) As Boolean
If Nb = 2 Then
IsPrime = True
ElseIf Nb < 2 Or Nb Mod 2 = 0 Then
Exit Function
Else
Dim i As Long
For i = 3 To Sqr(Nb) Step 2
If Nb Mod i = 0 Then Exit Function
Next
IsPrime = True
End If
End Function</syntaxhighlight>
{{out}}
<pre>
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
</pre>
==={{header|VBScript}}===
{{trans|QuickBASIC}}
<syntaxhighlight lang="vb">Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function
For n = 1 To 50
If IsPrime(n) Then
WScript.StdOut.Write n & " "
End If
Next</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
</pre>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="yabasic">for i = 1 to 99
if isPrime(i) print str$(i), " ";
next i
print
end
sub isPrime(v)
if v < 2 return False
if mod(v, 2) = 0 return v = 2
if mod(v, 3) = 0 return v = 3
d = 5
while d * d <= v
if mod(v, d) = 0 then return False else d = d + 2 : fi
wend
return True
end sub</syntaxhighlight>
==={{header|ZX Spectrum Basic}}===
<
20 INPUT "Enter number: ";n
30 IF n>1 THEN GO SUB 1000
40 IF p=0 THEN PRINT n;" is not prime!"
50 IF p<>0 THEN PRINT n;" is prime!"
Line 281 ⟶ 1,578:
1060 NEXT i
1070 RETURN
</syntaxhighlight>
{{out}}
<pre>
Line 287 ⟶ 1,584:
17 is prime!
119 is not prime!
137 is prime!</pre>
=={{header|
<syntaxhighlight lang="bc">/* Return 1 if n is prime, 0 otherwise */
define p(n) {
auto
if (n < 2) return(0)
if (n
if (n
for (i
return(1)
}</syntaxhighlight>
=={{header|BCPL}}==
<syntaxhighlight lang="bcpl">get "libhdr"
let sqrt(s) =
s <= 1 -> 1,
valof
$( let x0 = s >> 1
let x1 = (x0 + s/x0) >> 1
while x1 < x0
$( x0 := x1
x1 := (x0 + s/x0) >> 1
$)
resultis x0
$)
let isprime(n) =
n < 2 -> false,
(n & 1) = 0 -> n = 2,
valof
$( for i = 3 to sqrt(n) by 2
if n rem i = 0 resultis false
resultis true
$)
let start() be
$( for i=1 to 100
if isprime(i) then writef("%N ",i)
wrch('*N')
$)</syntaxhighlight>
{{out}}
<pre>2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</pre>
=={{header|Befunge}}==
Reads the value to test from stdin and outputs ''Yes'' if prime and ''No'' if not.
To avoid dealing with Befunge's limited data cells, the implementation is entirely stack-based. However, this requires compressing multiple values into a single stack cell, which imposes an upper limit of 1,046,529 (1023<sup>2</sup>), thus a maximum testable prime of 1,046,527.
<syntaxhighlight lang="befunge">&>:48*:** \1`!#^_2v
v_v#`\*:%*:*84\/*:*84::+<
v >::48*:*/\48*:*%%!#v_1^
>0"seY" >:#,_@#: "No">#0<</syntaxhighlight>
{{out}} (multiple runs)
<pre>0
No
17
Yes
49
No
97
Yes
1042441
No
1046527
Yes</pre>
=={{header|Bracmat}}==
<
= incs n I inc
. 4 2 4 2 4 6 2 6:?incs
Line 356 ⟶ 1,678:
)
)
& ;</
{{out}}
<pre>100000000003
Line 365 ⟶ 1,687:
100000000073
100000000091</pre>
=={{header|Brainf***}}==
<syntaxhighlight lang="bf">>->,[.>,]>-<++++++[-<+[---------<+]->+[->+]-<]>+<-<+[-<+]>>+[-<[->++++++++++<]>>
+]++++[->++++++++<]>.<+++++++[->++++++++++<]>+++.++++++++++.<+++++++++[->-------
--<]>--.[-]<<<->[->+>+<<]>>-[+<[[->>+>>+<<<<]>>[-<<+>>]<]>>[->-[>+>>]>[+[-<+>]>>
>]<<<<<]>[-]>[>+>]<<[-]+[-<+]->>>--]<[->+>+<<]>>>>>>>[-<<<<<->>>>>]<<<<<--[>++++
++++++[->+++++++++++<]>.+.+++++.>++++[->++++++++<]>.>]++++++++++[->+++++++++++<]
>++.++.---------.++++.--------.>++++++++++.</syntaxhighlight>
Explanation:
<syntaxhighlight lang="bf">>
->,[.>,]>-<++++++[-<+[---------<+]->+[->+]-<]>+<-<+[-<+]>>+[-<[->++++++++++<]>>+]< takes input
>++++[->++++++++<]>.<+++++++[->++++++++++<]>+++.++++++++++.<+++++++++[->---------<]>--.[-]<< " is "
<->
[->+>+<<]>>-[+<[[->>+>>+<<<<]>>[-<<+>>]<]>>[->-[>+>>]>[+[-<+>]>>>]<<<<<]>[-]>[>+>]<<[-]+[-<+]->>>--] finds # of divisors from 1 to n
<[->+>+<<]>>>>>>>[-<<<<<->>>>>]<<<<<--
[>++++++++++[->+++++++++++<]>.+.+++++.>++++[->++++++++<]>.>] "not "
++++++++++[->+++++++++++<]>++.++.---------.++++.--------.>++++++++++. "prime" new line</syntaxhighlight>
Will format as "# is/is not prime", naturally limited by cell size.
=={{header|Burlesque}}==
<syntaxhighlight lang="burlesque">fcL[2==</syntaxhighlight>
Implicit trial division is done by the ''fc'' function. It checks if the number has exactly two divisors.
Line 376 ⟶ 1,713:
Version not using the ''fc'' function:
<syntaxhighlight lang="burlesque">blsq ) 11^^2\/?dr@.%{0==}ayn!
1
blsq ) 12^^2\/?dr@.%{0==}ayn!
0
blsq ) 13^^2\/?dr@.%{0==}ayn!
1</syntaxhighlight>
Explanation. Given ''n'' generates a block containing ''2..n-1''. Calculates a block of modolus and check if it contains ''0''. If it contains ''0''
it is not a prime.
=={{header|C}}==
<
{
unsigned int p;
Line 398 ⟶ 1,732:
if (!(n % p)) return 0;
return 1;
}</
=={{header|C sharp|C#}}==
<syntaxhighlight lang="csharp">static bool isPrime(int n)
{
if (n <= 1) return false;
for (int i = 2; i * i <= n; i++)
if (n % i == 0) return false;
return true;
}</syntaxhighlight>
=={{header|C++}}==
<
bool is_prime(unsigned int n)
Line 413 ⟶ 1,756:
return false;
return true;
}</
=={{header|Chapel}}==
{{trans|C++}}
<
{
if n == 2 then
Line 437 ⟶ 1,770:
return false;
return true;
}</
=={{header|Clojure}}==
The function used in both versions:
<
Testing divisors are in range from '''3''' to '''√{{overline| n }} ''' with step '''2''':
<syntaxhighlight lang="clojure">(defn prime? [x]
(or (=
(and (< 1 x)
(odd? x)
(not-any? (partial divides? x)
(range 3 (inc (Math/sqrt x)) 2)))))
</syntaxhighlight>
Testing only prime divisors:
<syntaxhighlight lang="clojure">(declare prime?)
(def primes (filter prime? (range)))
(defn prime? [x]
(and (integer? x)
(< 1 x)
(not-any? (partial divides? x)
(take-while (partial >= (Math/sqrt x)) primes))))
</syntaxhighlight>
=={{header|CLU}}==
<syntaxhighlight lang="clu">isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
x1: int := (x0 + s/x0)/2
while x1 < x0 do
x0 := x1
x1 := (x0 + s/x0)/2
end
return(x0)
end isqrt
prime = proc (n: int) returns (bool)
if n<=2 then return(n=2) end
if n//2=0 then return(false) end
for d: int in int$from_to_by(3,isqrt(n),2) do
if n//d=0 then return(false) end
end
return(true)
end prime
start_up = proc ()
po: stream := stream$primary_input()
for i: int in int$from_to(1,100) do
if prime(i) then
stream$puts(po, int$unparse(i) || " ")
end
end
end start_up</syntaxhighlight>
{{out}}
<pre>2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</pre>
=={{header|CMake}}==
<
function(primep var n)
if(n GREATER 2)
Line 479 ⟶ 1,860:
set(${var} false PARENT_SCOPE) # n < 2 is not prime.
endif()
endfunction(primep)</
<
foreach(i -5 1 2 3 37 39)
primep(b ${i})
Line 489 ⟶ 1,870:
message(STATUS "${i} is _not_ prime.")
endif(b)
endforeach(i)</
=={{header|COBOL}}==
<
Program-Id. Primality-By-Subdiv.
Line 529 ⟶ 1,910:
Goback
.</
=={{header|CoffeeScript}}==
<
# simple prime detection using trial division, works
# for all integers
Line 543 ⟶ 1,924:
for i in [-1..100]
console.log i if is_prime i</
=={{header|Common Lisp}}==
<syntaxhighlight lang
"Is N prime?"
(and (> n 1)
(or (= n 2) (oddp n))
(loop for i from 3 to (isqrt n) by 2
never (zerop (rem n i)))))</
===Alternate solution===
I use [https://franz.com/downloads/clp/survey Allegro CL 10.1]
<syntaxhighlight lang="lisp">;; Project : Primality by trial division
(defun prime(n)
(setq flag 0)
(loop for i from 2 to (- n 1) do
(if (= (mod n i) 0)
(setq flag 1)))
(if (= flag 0)
(format t "~d is a prime number" n)
(format t "~d is not a prime number" n)))
(prime 7)
(prime 8)</syntaxhighlight>
Output:
7 is a prime number
8 is not a prime number
=={{header|Cowgol}}==
<syntaxhighlight lang="cowgol">include "cowgol.coh";
sub prime(n: uint32): (isprime: uint8) is
isprime := 1;
if n < 2 then
isprime := 0;
return;
end if;
if n & 1 == 0 then
if n != 2 then
isprime := 0;
end if;
return;
end if;
var factor: uint32 := 3;
while factor * factor <= n loop
if n % factor == 0 then
isprime := 0;
return;
end if;
factor := factor + 2;
end loop;
end sub;
var i: uint32 := 0;
while i <= 100 loop
if prime(i) != 0 then
print_i32(i);
print_nl();
end if;
i := i + 1;
end loop;</syntaxhighlight>
{{out}}
<pre>2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97</pre>
=={{header|Crystal}}==
Mathematicaly basis of Prime Generators
https://www.academia.edu/19786419/PRIMES-UTILS_HANDBOOK
https://www.academia.edu/42734410/Improved_Primality_Testing_and_Factorization_in_Ruby_revised
<syntaxhighlight lang="ruby">require "big"
require "benchmark"
# the simplest PG primality test using the P3 prime generator
# reduces the number space for primes to 2/6 (33.33%) of all integers
def primep3?(n) # P3 Prime Generator primality test
# P3 = 6*k + {5, 7} # P3 primes candidates (pc) sequence
n = n.to_big_i
return n | 1 == 3 if n < 5 # n: 0,1,4|false, 2,3|true
return false if n.gcd(6) != 1 # 1/3 (2/6) of integers are P3 pc
p = typeof(n).new(5) # first P3 sequence value
until p > isqrt(n)
return false if n % p == 0 || n % (p + 2) == 0 # if n is composite
p += 6 # first prime candidate for next kth residues group
end
true
end
# PG primality test using the P5 prime generator
# reduces the number space for primes to 8/30 (26.67%) of all integers
def primep5?(n) # P5 Prime Generator primality test
# P5 = 30*k + {7,11,13,17,19,23,29,31} # P5 primes candidates sequence
n = n.to_big_i
return [2, 3, 5].includes?(n) if n < 7 # for small and negative values
return false if n.gcd(30) != 1 # 4/15 (8/30) of integers are P5 pc
p = typeof(n).new(7) # first P5 sequence value
until p > isqrt(n)
return false if # if n is composite
n % (p) == 0 || n % (p+4) == 0 || n % (p+6) == 0 || n % (p+10) == 0 ||
n % (p+12) == 0 || n % (p+16) == 0 || n % (p+22) == 0 || n % (p+24) == 0
p += 30 # first prime candidate for next kth residues group
end
true
end
# PG primality test using the P7 prime generator
# reduces the number space for primes to 48/210 (22.86%) of all integers
def primep7?(n)
# P7 = 210*k + {11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
# 89,97,101,103,107,109,113,121,127,131,137,139,143,149,151,157,163,
# 167,169,173,179,181,187,191,193,197,199,209,211}
n = n.to_big_i
return [2, 3, 5, 7].includes?(n) if n < 11
return false if n.gcd(210) != 1 # 8/35 (48/210) of integers are P7 pc
p = typeof(n).new(11) # first P7 sequence value
until p > isqrt(n)
return false if
n % (p) == 0 || n % (p+2) == 0 || n % (p+6) == 0 || n % (p+8) == 0 ||
n % (p+12) == 0 || n % (p+18) == 0 || n % (p+20) == 0 || n % (p+26) == 0 ||
n % (p+30) == 0 || n % (p+32) == 0 || n % (p+36) == 0 || n % (p+42) == 0 ||
n % (p+48) == 0 || n % (p+50) == 0 || n % (p+56) == 0 || n % (p+60) == 0 ||
n % (p+62) == 0 || n % (p+68) == 0 || n % (p+72) == 0 || n % (p+78) == 0 ||
n % (p+86) == 0 || n % (p+90) == 0 || n % (p+92) == 0 || n % (p+96) == 0 ||
n % (p+98) == 0 || n % (p+102) == 0 || n % (p+110) == 0 || n % (p+116) == 0 ||
n % (p+120) == 0 || n % (p+126) == 0 || n % (p+128) == 0 || n % (p+132) == 0 ||
n % (p+138) == 0 || n % (p+140) == 0 || n % (p+146) == 0 || n % (p+152) == 0 ||
n % (p+156) == 0 || n % (p+158) == 0 || n % (p+162) == 0 || n % (p+168) == 0 ||
n % (p+170) == 0 || n % (p+176) == 0 || n % (p+180) == 0 || n % (p+182) == 0 ||
n % (p+186) == 0 || n % (p+188) == 0 || n % (p+198) == 0 || n % (p+200) == 0
p += 210 # first prime candidate for next kth residues group
end
true
end
# Newton's method for integer squareroot
def isqrt(n)
raise ArgumentError.new "Input must be non-negative integer" if n < 0
return n if n < 2
bits = n.bit_length
one = typeof(n).new(1) # value 1 of type self
x = one << ((bits - 1) >> 1) | n >> ((bits >> 1) + 1)
while (t = n // x) < x; x = (x + t) >> 1 end
x # output is same integer class as input
end
# Benchmarks to test for various size primes
p = 541
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
puts
end
p = 1000003
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
puts
end
p = 2147483647i32 # largest I32 prime
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
puts
end
p = 4294967291u32 # largest U32 prime
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
puts
end
p = 4294967311 # first prime > 2**32
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
puts
end</syntaxhighlight>
{{out}}
<pre>p = 541
primep3? 290.17k ( 3.45µs) (± 2.76%) 1.35kB/op 1.64× slower
primep5? 476.47k ( 2.10µs) (± 1.75%) 802B/op fastest
primep7? 128.44k ( 7.79µs) (± 2.82%) 2.66kB/op 3.71× slower
p = 1000003
primep3? 11.24k ( 88.97µs) (± 2.34%) 33.9kB/op 2.48× slower
primep5? 21.91k ( 45.64µs) (± 2.88%) 16.6kB/op 1.27× slower
primep7? 27.83k ( 35.94µs) (± 2.68%) 11.9kB/op fastest
p = 2147483647
primep3? 105.11 ( 9.51ms) (± 3.25%) 3.89MB/op 5.56× slower
primep5? 317.49 ( 3.15ms) (± 2.40%) 1.2MB/op 1.84× slower
primep7? 584.92 ( 1.71ms) (± 3.09%) 591kB/op fastest
p = 4294967291
primep3? 168.56 ( 5.93ms) (± 2.39%) 2.17MB/op 2.69× slower
primep5? 349.24 ( 2.86ms) (± 2.86%) 1.03MB/op 1.30× slower
primep7? 454.08 ( 2.20ms) (± 2.62%) 739kB/op fastest
p = 4294967311
primep3? 84.61 ( 11.82ms) (± 2.35%) 4.68MB/op 5.02× slower
primep5? 248.62 ( 4.02ms) (± 2.21%) 1.54MB/op 1.71× slower
primep7? 424.61 ( 2.36ms) (± 2.73%) 813kB/op fastest
</pre>
=={{header|D}}==
===Simple Version===
<
bool
return
return false;
for(T i = 3; i <= real(n).sqrt; i += 2)
if (n % i == 0)
return false;
return true;
}
void main() {
iota(2, 40).filter!isPrime1.writeln;
}</syntaxhighlight>
{{out}}
===Version with excluded multiplies of 2 and 3===
Same output.
<syntaxhighlight lang="d">bool isPrime2(It)(in It n) pure nothrow {
// Adapted from: http://www.devx.com/vb2themax/Tip/19051
// Test 1, 2, 3 and multiples of 2 and 3:
if (n == 2 || n == 3)
return true;
else if (n < 2 || n % 2 == 0 || n % 3 == 0)
return false;
// We can now avoid to consider multiples of 2 and 3. This
// can be done really simply by starting at 5 and
// incrementing by 2 and 4 alternatively, that is:
// 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, ...
// We don't need to go higher than the square root of the n.
for (It div = 5, inc = 2; div ^^ 2 <= n; div += inc, inc = 6 - inc)
if (n % div == 0)
return false;
return true;
}
void main() {
import std.stdio, std.algorithm, std.range;
iota(2, 40).filter!isPrime2.writeln;
}</syntaxhighlight>
===Two Way Test===
Odd divisors is generated both from increasing and decreasing sequence, may improve performance for numbers that have large minimum factor.
Same output.
<
bool isPrime3(T)(in T n) pure nothrow {
if (n % 2 == 0 || n <= 1)
return n == 2;
T head = 3, tail = (cast(T)
for ( ; head <= tail ; head +=2, tail -= 2)
if ((n % head) == 0 || (n % tail) == 0)
Line 624 ⟶ 2,238:
}
void main() {
iota(2, 40).filter!isPrime3
}</
=={{header|
<syntaxhighlight lang="dart">import 'dart:math';
bool isPrime(int n) {
if (n <= 1) return false;
if (n == 2) return true;
for (int i = 2; i <= sqrt(n); ++i) if (n % i == 0) return false;
return true;
}
void main() {
for (int i = 1; i <= 99; ++i) if (isPrime(i)) print('$i ');
}</syntaxhighlight>
=={{header|Delphi}}==
=== First ===
<
var
I: Integer;
Line 648 ⟶ 2,275:
Break;
end;
end;</
=== Second ===
<
var
i: integer;
Line 665 ⟶ 2,292:
until i > Sqrt(x);
Result := True;
end;</
=={{header|Draco}}==
<syntaxhighlight lang="draco">proc prime(word n) bool:
word factor;
bool composite;
if n<=4 then
n=2 or n=3
elif n&1 = 0 then
false
else
factor := 3;
composite := false;
while not composite and factor*factor <= n do
composite := n % factor = 0;
factor := factor + 2
od;
not composite
fi
corp
proc main() void:
word i;
for i from 0 upto 100 do
if prime(i) then
writeln(i)
fi
od
corp</syntaxhighlight>
{{out}}
<pre>2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97</pre>
=={{header|E}}==
{{trans|D}}
<
if (n == 2) {
return true
Line 684 ⟶ 2,365:
return true
}
}</
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
func isprim n .
if n < 2
return 0
.
if n mod 2 = 0 and n > 2
return 0
.
i = 3
sq = sqrt n
while i <= sq
if n mod i = 0
return 0
.
i += 2
.
return 1
.
print isprim 1995937
</syntaxhighlight>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">(lib 'sequences)
;; Try divisors iff n = 2k + 1
(define (is-prime? p)
(cond
[(< p 2) #f]
[(zero? (modulo p 2)) (= p 2)]
[else
(for/and ((d [3 5 .. (1+ (sqrt p))] )) (!zero? (modulo p d)))]))
(filter is-prime? (range 1 100))
→ (2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97)
;; Improve performance , try divisors iff n = 6k+1 or n = 6k+5
(define (is-prime? p)
(cond
[(< p 2) #f]
[(zero? (modulo p 2)) (= p 2)]
[(zero? (modulo p 3)) (= p 3)]
[(zero? (modulo p 5)) (= p 5)]
[else ;; step 6 : try divisors 6n+1 or 6n+5
(for ((d [7 13 .. (1+ (sqrt p))] ))
#:break (zero? (modulo p d)) => #f
#:break (zero? (modulo p (+ d 4))) => #f
#t )]))
(filter is-prime? (range 1 100))
→ (2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97)</syntaxhighlight>
=={{header|Eiffel}}==
<syntaxhighlight lang="eiffel">class
APPLICATION
create
make
feature
make
-- Tests the feature is_prime.
do
io.put_boolean (is_prime (1))
io.new_line
io.put_boolean (is_prime (2))
io.new_line
io.put_boolean (is_prime (3))
io.new_line
io.put_boolean (is_prime (4))
io.new_line
io.put_boolean (is_prime (97))
io.new_line
io.put_boolean (is_prime (15589))
io.new_line
end
is_prime (n: INTEGER): BOOLEAN
-- Is 'n' a prime number?
require
positiv_input: n > 0
local
i: INTEGER
max: REAL_64
math: DOUBLE_MATH
do
create math
if n = 2 then
Result := True
elseif n <= 1 or n \\ 2 = 0 then
Result := False
else
Result := True
max := math.sqrt (n)
from
i := 3
until
i > max
loop
if n \\ i = 0 then
Result := False
end
i := i + 2
end
end
end
end</syntaxhighlight>
<pre>False
True
True
False
True
False</pre>
=={{header|Elixir}}==
{{trans|Erlang}}
<syntaxhighlight lang="elixir">defmodule RC do
def is_prime(2), do: true
def is_prime(n) when n<2 or rem(n,2)==0, do: false
def is_prime(n), do: is_prime(n,3)
def is_prime(n,k) when n<k*k, do: true
def is_prime(n,k) when rem(n,k)==0, do: false
def is_prime(n,k), do: is_prime(n,k+2)
end
IO.inspect for n <- 1..50, RC.is_prime(n), do: n</syntaxhighlight>
{{out}}
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
=={{header|Emacs Lisp}}==
{{libheader|cl-lib}}
<syntaxhighlight lang="lisp">(defun prime (a)
(not (or (< a 2)
(cl-loop for x from 2 to (sqrt a)
when (zerop (% a x))
return t))))</syntaxhighlight>
More concise, a little bit faster:
<syntaxhighlight lang="lisp">(defun prime2 (a)
(and (> a 1)
(cl-loop for x from 2 to (sqrt a)
never (zerop (% a x)))))</syntaxhighlight>
A little bit faster:
<syntaxhighlight lang="lisp">(defun prime3 (a)
(and (> a 1)
(or (= a 2) (cl-oddp a))
(cl-loop for x from 3 to (sqrt a) by 2
never (zerop (% a x)))))</syntaxhighlight>
More than 2 times faster, than the previous, doesn't use <tt>loop</tt> macro:
<syntaxhighlight lang="lisp">(defun prime4 (a)
(not (or (< a 2)
(cl-some (lambda (x) (zerop (% a x))) (number-sequence 2 (sqrt a))))))</syntaxhighlight>
Almost 2 times faster, than the previous:
<syntaxhighlight lang="lisp">(defun prime5 (a)
(not (or (< a 2)
(and (/= a 2) (cl-evenp a))
(cl-some (lambda (x) (zerop (% a x))) (number-sequence 3 (sqrt a) 2)))))</syntaxhighlight>
=={{header|Erlang}}==
<
is_prime(N) when N < 2 orelse N rem 2 == 0 -> false;
is_prime(N) -> is_prime(N,3).
Line 693 ⟶ 2,538:
is_prime(N,K) when K*K > N -> true;
is_prime(N,K) when N rem K == 0 -> false;
is_prime(N,K) -> is_prime(N,K+2).</
=={{header|ERRE}}==
<syntaxhighlight lang="erre">PROGRAM PRIME_TRIAL
PROCEDURE ISPRIME(N%->OK%)
LOCAL T%
IF N%<=1 THEN OK%=FALSE EXIT PROCEDURE END IF
IF N%<=3 THEN OK%=TRUE EXIT PROCEDURE END IF
IF (N% AND 1)=0 THEN OK%=FALSE EXIT PROCEDURE END IF
FOR T%=3 TO SQR(N%) STEP 2 DO
IF N% MOD T%=0 THEN OK%=FALSE EXIT PROCEDURE END IF
END FOR
OK%=TRUE
END PROCEDURE
BEGIN
FOR I%=1 TO 100 DO
ISPRIME(I%->OK%)
IF OK% THEN PRINT(i%;"is prime") END IF
END FOR
END PROGRAM</syntaxhighlight>
{{out}}
2 is prime
3 is prime
5 is prime
7 is prime
11 is prime
13 is prime
17 is prime
19 is prime
23 is prime
29 is prime
31 is prime
37 is prime
41 is prime
43 is prime
47 is prime
53 is prime
59 is prime
61 is prime
67 is prime
71 is prime
73 is prime
79 is prime
83 is prime
89 is prime
97 is prime
=={{header|Euphoria}}==
<
if n<=2 or remainder(n,2)=0 then
return 0
Line 707 ⟶ 2,601:
return 1
end if
end function</
=={{header|F Sharp|F#}}==
<syntaxhighlight lang="fsharp">open NUnit.Framework
open FsUnit
let inline isPrime n = not ({uint64 2..uint64 (sqrt (double n))} |> Seq.exists (fun (i:uint64) -> uint64 n % i = uint64 0))
[<Test>]
let ``Validate that 2 is prime`` () =
isPrime 2 |> should equal true
[<Test>]
let ``Validate that 4 is not prime`` () =
isPrime 4 |> should equal false
[<Test>]
let ``Validate that 3 is prime`` () =
isPrime 3 |> should equal true
[<Test>]
let ``Validate that 9 is not prime`` () =
isPrime 9 |> should equal false
[<Test>]
let ``Validate that 5 is prime`` () =
isPrime 5 |> should equal true
[<Test>]
let ``Validate that 277 is prime`` () =
isPrime 277 |> should equal true</syntaxhighlight>
{{out}}
> isPrime 1111111111111111111UL;;
val it : bool = true
and if you want to test really big numbers, use System.Numerics.BigInteger, but it's slower:
<syntaxhighlight lang="fsharp">
let isPrimeI x =
if x < 2I then false else
if x = 2I then true else
if x % 2I = 0I then false else
let rec test n =
if n * n > x then true else
if x % n = 0I then false else test (n + 2I) in test 3I</syntaxhighlight>
If you have a lot of prime numbers to test, caching a sequence of primes can speed things up considerably, so you only have to do the divisions against prime numbers.
<syntaxhighlight lang="fsharp">let rec primes = Seq.cache(Seq.append (seq[ 2; 3; 5 ]) (Seq.unfold (fun state -> Some(state, state + 2)) 7 |> Seq.filter (fun x -> IsPrime x)))
and IsPrime number =
let rec IsPrimeCore number current limit =
let cprime = primes |> Seq.nth current
if cprime >= limit then
true
else if number % cprime = 0 then
false
else
IsPrimeCore number (current + 1) (number/cprime)
if number = 2 then
true
else if number < 2 then
false
else
IsPrimeCore number 0 number</syntaxhighlight>
=={{header|Factor}}==
<
: prime? ( n -- ? )
Line 717 ⟶ 2,672:
{ [ dup even? ] [ 2 = ] }
[ 3 over sqrt 2 <range> [ mod 0 > ] with all? ]
} cond ;</
=={{header|FALSE}}==
<
3[\$@$@1+\$*>][\$@$@$@$@\/*=[%\~\$]?2+]#%
]?]?%]p:</
=={{header|Forth}}==
<syntaxhighlight lang="forth">: prime? ( n -- f )
dup 2 < if drop false
else dup 2 = if drop true
Line 782 ⟶ 2,691:
then 2 +
repeat 2drop true
then then then ;</
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<
LOGICAL :: isPrime
INTEGER, INTENT(IN) :: number
Line 804 ⟶ 2,713:
END DO
END IF
END FUNCTION</
=={{header|Frink}}==
It is unnecessary to write this function because Frink has an efficient <CODE>isPrime[x]</CODE> function to test primality of arbitrarily-large integers. Here is a version that works for arbitrarily-large integers. Beware some of these solutions that calculate up to <CODE>sqrt[x]</CODE> but because of floating-point error the square root is slightly smaller than the true square root!
<syntaxhighlight lang="frink">isPrimeByTrialDivision[x] :=
{
for p = primes[]
{
if p*p > x
return true
if x mod p == 0
return false
}
return true
}</syntaxhighlight>
=={{header|FunL}}==
<syntaxhighlight lang="funl">import math.sqrt
def
isPrime( 2 ) = true
isPrime( n )
| n < 3 or 2|n = false
| otherwise = (3..int(sqrt(n)) by 2).forall( (/|n) )
(10^10..10^10+50).filter( isPrime ).foreach( println )</syntaxhighlight>
{{out}}
10000000019
10000000033
=={{header|GAP}}==
<
local k, m;
if n < 5 then
Line 867 ⟶ 2,767:
Filtered([1 .. 100], IsPrimeTrial);
# [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 ]</
=={{header|Go}}==
<
if n < 0
switch {
case n == 2:
return true
case n < 2 || n % 2 == 0:
return false
default:
for i = 3; i*i <= n; i += 2 {
if n % i == 0 { return false }
}
}
return true
}</syntaxhighlight>
Or, using recursion:
<syntaxhighlight lang="go">func IsPrime(n int) bool {
if n < 0 { n = -n }
if n <= 2 {
return n == 2
}
return n % 2 != 0 && isPrime_r(n, 3)
}
func isPrime_r(n, i int) bool {
if i*i <= n {
return n % i != 0 && isPrime_r(n, i+2)
}
return true
}</syntaxhighlight>
=={{header|Groovy}}==
<
it == 2 ||
it > 1 &&
Line 887 ⟶ 2,810:
}
(0..20).grep(isPrime)</
{{out}}
=={{header|Haskell}}==
(used [[Emirp_primes#List-based|here]] and [[Sequence_of_primes_by_Trial_Division#Haskell|here]]). The basic divisibility test by odd numbers:
<
Testing by prime numbers only is faster. Primes list is saved for reuse. Precalculation of primes pays off if testing more than just a few numbers, and/or primes are generated efficiently enough:
<
-- primeNums = filter (noDivsBy [2..]) [2..]
-- = 2 : filter (noDivsBy [3,5..]) [3,5..]
primeNums = 2 : 3 : filter (noDivsBy $ tail primeNums) [5,7..]
isPrime n = n > 1 && noDivsBy primeNums n</
Any increasing ''unbounded'' sequence of numbers that includes all primes
A less efficient, more basic variant:
<
The following is an attempt at improving it, resulting in absolutely worst performing prime testing code I've ever seen, ever. A curious oddity.
<syntaxhighlight lang="haskell">isPrime n = n > 1 && []==[i | i <- [2..n-1], isPrime i && rem n i == 0]</syntaxhighlight>
=={{header|HicEst}}==
<
Euler = n^2 + n + 41
IF( Prime(Euler) == 0 ) WRITE(Messagebox) Euler, ' is NOT prime for n =', n
Line 950 ⟶ 2,852:
Prime = 1
ENDIF
END</
=={{header|Icon}} and {{header|Unicon}}==
Procedure shown without a main program.
<
if not n = integer(n) | n < 2 then fail # ensure n is an integer greater than 1
every if 0 = (n % (2 to sqrt(n))) then fail
return n
end</
=={{header|J}}==
{{eff note|J|1&p:}}
<
=={{header|Java}}==
<
if(a == 2){
return true;
Line 976 ⟶ 2,878:
}
return true;
}</
===By Regular Expression===
<
return !new String(new char[n]).matches(".?|(..+?)\\1+");
}</
=={{header|JavaScript}}==
<
if (n == 2 || n == 3 || n == 5 || n == 7) {
return true;
} else if ((n < 2) || (n % 2 == 0)) {
Line 995 ⟶ 2,897:
return true;
}
}</
=={{header|Joy}}==
<syntaxhighlight lang joy>DEFINE prime ==
2 [[dup * >] nullary [rem 0 >] dip and]
[succ] while dup * <.</syntaxhighlight>
=={{header|jq}}==
<tt> def is_prime:
if . == 2 then
else 2 < . and . % 2 == 1 and
. as $in
| (($in + 1) | sqrt) as $m
| (((($m - 1) / 2) | floor) + 1) as $max
| all( range(1; $max) ; $in % ((2 * .) + 1) > 0 )
end;</tt>
Example -- the command line is followed by alternating lines of input and output:
<tt> $ jq -f is_prime.jq
-2
false
1
false
2
true
100
false</tt>
''Note: if your jq does not have <tt>all</tt>, the following will suffice:''
def all(generator; condition):
reduce generator as $i (true; . and ($i|condition));
=={{header|Julia}}==
Julia already has an <tt>isprime</tt> function, so this function has the verbose name <tt>isprime_trialdivision</tt> to avoid overriding the built-in function. Note this function relies on the fact that Julia skips <tt>for</tt>-loops having invalid ranges. Otherwise the function would have to include additional logic to check the odd numbers less than 9.
<syntaxhighlight lang="julia">function isprime_trialdivision{T<:Integer}(n::T)
1 < n || return false
n != 2 || return true
isodd(n) || return false
for i in 3:isqrt(n)
n%i != 0 || return false
end
return true
end
n = 100
a = filter(isprime_trialdivision, [1:n])
if all(a .== primes(n))
println("The primes <= ", n, " are:\n ", a)
else
println("The function does not accurately calculate primes.")
end</syntaxhighlight>
{{out}}
The primes <= 100 are:
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
=={{header|K}}==
<
&isprime'!100
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</
=={{header|
<syntaxhighlight lang="scala">// version 1.1.2
fun isPrime(n: Int): Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
val limit = Math.sqrt(n.toDouble()).toInt()
return (3..limit step 2).none { n % it == 0 }
}
fun main(args: Array<String>) {
// test by printing all primes below 100 say
(2..99).filter { isPrime(it) }.forEach { print("$it ") }
}</syntaxhighlight>
{{out}}
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
1) the simplest
{def isprime1
{def isprime1.loop
{lambda {:n :m :i}
{if {> :i :m}
then true
else {if {= {% :n :i} 0}
then false
else {isprime1.loop :n :m {+ :i 1}} }
}}}
{lambda {:n}
{isprime1.loop :n {sqrt :n} 2}
}}
-> isprime1
2) slightly improved
{def isprime2
{def isprime2.loop
{lambda {:n :m :i}
{if {> :i :m}
then true
else {if {= {% :n :i} 0}
then false
else {isprime2.loop :n :m {+ :i 2}}
}}}}
{lambda {:n}
{if {or {= :n 2} {= :n 3} {= :n 5} {= :n 7}}
then true
else {if {or {< : n 2} {= {% :n 2} 0}}
then false
else {isprime2.loop :n {sqrt :n} 3}
}}}}
-> isprime2
3) testing
{isprime1 1299709} -> stackoverflow on my iPad Pro
{isprime2 1299709} -> true
{def primesTo
{lambda {:f :n}
{S.replace \s by space in
{S.map {{lambda {:f :i} {if {:f :i} then :i else}} :f}
{S.serie 2 :n}}} }}
-> primesTo
{primesTo isprime1 100}
-> 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 in 25ms
{primesTo isprime2 100}
-> 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 in 20ms
{primesTo isprime1 1000000} in about 30000ms
{primesTo isprime2 1000000} in about 15000ms
</syntaxhighlight>
=={{header|langur}}==
=== Functional ===
{{trans|Raku}}
following the Raku example, which states, "Integer $i is prime if it is greater than one and is divisible by none of 2, 3, up to the square root of $i" (plus an adjustment for the prime number 2)
Below, we use an implied parameter (.i) on the .isPrime function.
<syntaxhighlight lang="langur">val .isPrime = fn(.i) {
.i == 2 or .i > 2 and
not any fn(.x) { .i div .x }, pseries 2 .. .i ^/ 2
}
writeln filter .isPrime, series 100</syntaxhighlight>
=== Recursive ===
{{trans|Go}}
<syntaxhighlight lang="langur">val .isPrime = fn(.i) {
val .n = abs(.i)
if .n <= 2: return .n == 2
val .chkdiv = fn(.n, .i) {
if .i * .i <= .n {
return .n ndiv .i and self(.n, .i+2)
}
return true
}
return .n ndiv 2 and .chkdiv(.n, 3)
}
writeln filter .isPrime, series 100</syntaxhighlight>
{{out}}
<pre>[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]</pre>
=={{header|Lingo}}==
<syntaxhighlight lang="lingo">on isPrime (n)
if n<=1 or (n>2 and n mod 2=0) then return FALSE
sq = sqrt(n)
repeat with i = 3 to sq
if n mod i = 0 then return FALSE
end repeat
return TRUE
end</syntaxhighlight>
<syntaxhighlight lang="lingo">primes = []
repeat with i = 0 to 100
if isPrime(i) then primes.add(i)
end repeat
put primes</syntaxhighlight>
{{out}}
-- [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
=={{header|Logo}}==
<
if :n < 2 [output "false]
if :n = 2 [output "true]
Line 1,042 ⟶ 3,094:
for [i 3 [sqrt :n] 2] [if equal? 0 modulo :n :i [output "false]]
output "true
end</
=={{header|LSE64}}==
<
2dup : over over
even? : 1 & 0 =
Line 1,059 ⟶ 3,111:
prime? : dup even? then drop false
prime? : dup 2 = then drop true
prime? : dup 2 < then drop false</
=={{header|Lua}}==
<
if n <= 1 or ( n ~= 2 and n % 2 == 0 ) then
return false
Line 1,074 ⟶ 3,126:
return true
end</
Type of number Decimal.
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
Module Primality_by_trial_division {
Inventory Known1=2@, 3@
IsPrime=lambda Known1 (x as decimal) -> {
=false
if exist(Known1, x) then =true : exit
if x<=5 OR frac(x) then {if x == 2 OR x == 3 OR x == 5 then Append Known1, x : =true
Break}
if frac(x/2) else exit
if frac(x/3) else exit
x1=sqrt(x):d = 5@
do
if frac(x/d) else exit
d += 2: if d>x1 then Append Known1, x : =true : exit
if frac(x/d) else exit
d += 4: if d<= x1 else Append Known1, x : =true: exit
always
}
i=2
While Len(Known1)<20
dummy=Isprime(i)
i++
End While
Print "first ";len(known1);" primes"
Print Known1
Print "From 110 to 130"
count=0
For i=110 to 130
If isPrime(i) Then Print i, : count++
Next
Print
Print "Found ";count;" primes"
}
Primality_by_trial_division
</syntaxhighlight>
=={{header|M4}}==
<
`ifelse(eval($2*$2>$1),1,
1,
Line 1,091 ⟶ 3,182:
isprime(9)
isprime(11)</
{{out}}
0
1
=={{header|MAD}}==
<syntaxhighlight lang="MAD"> NORMAL MODE IS INTEGER
INTERNAL FUNCTION(N)
ENTRY TO PRIME.
WHENEVER N.L.2, FUNCTION RETURN 0B
WHENEVER N.E.N/2*2, FUNCTION RETURN N.E.2
THROUGH TRIAL, FOR FAC=3, 2, FAC*FAC.G.N
TRIAL WHENEVER N.E.N/FAC*FAC, FUNCTION RETURN 0B
FUNCTION RETURN 1B
END OF FUNCTION
PRINT COMMENT $ PRIMES UNDER 100 $
THROUGH CAND, FOR C=0, 1, C.G.100
CAND WHENEVER PRIME.(C), PRINT FORMAT PR,C
VECTOR VALUES PR = $ I3*$
END OF PROGRAM</syntaxhighlight>
{{out}}
<pre>PRIMES UNDER 100
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97</pre>
=={{header|Maple}}==
This could be coded in myriad ways; here is one.
<syntaxhighlight lang="maple">TrialDivision := proc( n :: integer )
if n <= 1 then
false
Line 1,116 ⟶ 3,250:
true
end if
end proc:</syntaxhighlight>
Using this to pick off the primes up to 30, we get:
<syntaxhighlight lang="maple">> select( TrialDivision, [seq]( 1 .. 30 ) );
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]</syntaxhighlight>
Here is a way to check that TrialDivision above agrees with Maple's built-in primality test (isprime).
<syntaxhighlight lang="maple">> N := 10000: evalb( select( TrialDivision, [seq]( 1 .. N ) ) = select( isprime, [seq]( 1 .. N ) ) );
true</syntaxhighlight>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
If[n <= 1, Return[False]];
If[n
For[k = 3, k <= Sqrt[n], k += 2, If[Mod[n, k] ==
Return[True]]</syntaxhighlight>
=={{header|MATLAB}}==
<
if n == 2
Line 1,159 ⟶ 3,284:
isPrime = all(mod(n, (3:round(sqrt(n))) ));
end</
{{out|Sample output}}
<
ans =
0 1 1 0 1 0 1 0 0 0 1 0 1 0</
=={{header|
<syntaxhighlight lang="maxima">isprme(n):= catch(
for k: 2 thru sqrt(n) do if mod(n, k)=0 then throw(false),
true);
map(isprme, [2, 3, 4, 65, 100, 181, 901]);
/* [true, true, false, false, false, true, false] */</syntaxhighlight>
=={{header|min}}==
{{works with|min|0.19.3}}
<syntaxhighlight lang="min">(
:n 3 :i n sqrt :m true :p
(i m <=) (
(n i mod 0 ==) (m @i false @p) when
i 2 + @i
) while
) :_prime? ; helper function
(
(
((2 <) (false))
((dup even?) (2 ==))
((true) (_prime?))
) case
) :prime?</syntaxhighlight>
=={{header|Miranda}}==
<syntaxhighlight lang="miranda">main :: [sys_message]
main = [Stdout (show (filter prime [1..100])),
Stdout "\n"]
prime :: num->bool
prime n = n=2 \/ n=3, if n<=4
= False, if n mod 2=0
= #[d | d<-[3, 5..sqrt n]; n mod d=0]=0, otherwise</syntaxhighlight>
{{out}}
<pre>[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]</pre>
=={{header|МК-61/52}}==
<syntaxhighlight lang="text">П0
3 П4 ИП0 ИП4 / {x} x#0
ИП0 КвКор ИП4 - x<0 16 1 С/П 0 С/П</
=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">MODULE TrialDivision;
FROM InOut IMPORT WriteCard, WriteLn;
CONST
Max = 100;
VAR
i: CARDINAL;
PROCEDURE prime(n: CARDINAL): BOOLEAN;
VAR
factor: CARDINAL;
BEGIN
IF n <= 4 THEN
RETURN (n = 2) OR (n = 3)
ELSIF n MOD 2 = 0 THEN
RETURN FALSE
ELSE
factor := 3;
WHILE factor * factor <= n DO
IF n MOD factor = 0 THEN
RETURN FALSE
END;
INC(factor, 2)
END
END;
RETURN TRUE
END prime;
BEGIN
FOR i := 0 TO Max DO
IF prime(i) THEN
WriteCard(i,3);
WriteLn
END
END
END TrialDivision.</syntaxhighlight>
{{out}}
<pre> 2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97</pre>
=={{header|MUMPS}}==
<
QUIT:(N=2) 1
NEW I,
SET
IF
KILL I
QUIT
Usage (0 is false, nonzero is true):
<pre>USER>W $$ISPRIME^ROSETTA(2)
Line 1,208 ⟶ 3,416:
1
USER>W $$ISPRIME^ROSETTA(97)
7
USER>W $$ISPRIME^ROSETTA(99)
0</pre>
=={{header|NetRexx}}==
<
options replace format comments java crossref savelog symbols nobinary
Line 1,278 ⟶ 3,486:
method isFalse public static returns boolean
return \isTrue</
{{out}}
<pre>$ java -cp . RCPrimality
List of prime numbers from 1 to 100:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
Line 1,310 ⟶ 3,517:
List of prime numbers from 100 to -57:
97,89,83,79,73,71,67,61,59,53,47,43,41,37,31,29,23,19,17,13,11,7,5,3,2
Total number of primes: 25</pre>
===[[#REXX|Rexx]] version reimplemented in [[NetRexx]]===
{{trans|REXX}}
<
options replace format comments java crossref savelog symbols nobinary
Line 1,345 ⟶ 3,551:
end
return 1 /*I'm exhausted, it's prime!*/</
=={{header|newLISP}}==
Short-circuit evaluation ensures that the many Boolean expressions are calculated in the right order so as not to waste time.
<syntaxhighlight lang="newlisp">; Here are some simpler functions to help us:
(define (divisible? larger-number smaller-number)
(zero? (% larger-number smaller-number)))
(define (int-root number)
(floor (sqrt number)))
(define (even-prime? number)
(= number 2))
; Trial division for odd numbers
(define (find-odd-factor? odd-number)
(catch
(for (possible-factor 3 (int-root odd-number) 2)
(if (divisible? odd-number possible-factor)
(throw true)))))
(define (odd-prime? number)
(and
(odd? number)
(or
(= number 3)
(and
(> number 3)
(not (find-odd-factor? number))))))
; Now for the final overall Boolean function.
(define (is-prime? possible-prime)
(or
(even-prime? possible-prime)
(odd-prime? possible-prime)))
; Let's use this to actually find some prime numbers.
(println (filter is-prime? (sequence 1 100)))
(exit)</syntaxhighlight>
{{Output}}
(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97)
=={{header|Nim}}==
Here are three ways to test primality using trial division.
<syntaxhighlight lang="nim">import sequtils, math
proc prime(a: int): bool =
if a == 2: return true
if a < 2 or a mod 2 == 0: return false
for i in countup(3, sqrt(a.float).int, 2):
if a mod i == 0:
return false
return true
proc prime2(a: int): bool =
result = not (a < 2 or any(toSeq(2 .. sqrt(a.float).int), a mod it == 0))
proc prime3(a: int): bool =
if a == 2: return true
if a < 2 or a mod 2 == 0: return false
return not any(toSeq countup(3, sqrt(a.float).int, 2), a mod it == 0)
for i in 2..30:
echo i, " ", prime(i)</syntaxhighlight>
{{out}}
<pre>2 true
3 true
4 false
5 true
6 false
7 true
8 false
9 false
10 false
11 true
12 false
13 true
14 false
15 false
16 false
17 true
18 false
19 true
20 false
21 false
22 false
23 true
24 false
25 false
26 false
27 false
28 false
29 true
30 false</pre>
=={{header|Objeck}}==
<
if(n <= 1) {
return false;
Line 1,360 ⟶ 3,665:
return true;
}</
=={{header|OCaml}}==
<
if n
then n lor 1 = 3
else n land 1
=={{header|Octave}}==
This function works on vectors and matrix.
<
for r = 1:rows(n)
for c = 1:columns(n)
Line 1,399 ⟶ 3,702:
p = [1:100];
pv = isthisprime(p);
disp(p( pv ));</
=={{header|Oforth}}==
<syntaxhighlight lang="oforth">Integer method: isPrime
| i |
self 1 <= ifTrue: [ false return ]
self 3 <= ifTrue: [ true return ]
self isEven ifTrue: [ false return ]
3 self sqrt asInteger for: i [ self i mod ifzero: [ false return ] ]
true ;</syntaxhighlight>
{{out}}
<pre>#isPrime 1000 seq filter println
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 8
9, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181
, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281
, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503
, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619
, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743
, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863
, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
]</pre>
=={{header|Ol}}==
<syntaxhighlight lang="scheme">
(define (prime? number)
(define max (sqrt number))
(define (loop divisor)
(or (> divisor max)
(and (> (modulo number divisor) 0)
(loop (+ divisor 2)))))
(or (= number 1)
(= number 2)
(and
(> (modulo number 2) 0)
(loop 3))))
</syntaxhighlight>
Testing:
<syntaxhighlight lang="scheme">
; first prime numbers less than 100
(for-each (lambda (n)
(if (prime? n)
(display n))
(display " "))
(iota 100))
(print)
; few more sintetic tests
(for-each (lambda (n)
(print n " - prime? " (prime? n)))
'(
1234567654321 ; 1111111 * 1111111
679390005787 ; really prime, I know that
679390008337 ; same
666810024403 ; 680633 * 979691 (multiplication of two prime numbers)
12345676543211234567654321
12345676543211234567654321123456765432112345676543211234567654321123456765432112345676543211234567654321
))
</syntaxhighlight>
{{out}}
<pre> 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
1234567654321 - prime? #false
679390005787 - prime? #true
679390008337 - prime? #true
666810024403 - prime? #false
12345676543211234567654321 - prime? #false
12345676543211234567654321123456765432112345676543211234567654321123456765432112345676543211234567654321 - prime? #false
</pre>
=={{header|Oz}}==
<syntaxhighlight lang="oz"> fun {Prime N}
local IPrime in
fun {IPrime N Acc}
if N < Acc*Acc then true
elseif (N mod Acc) == 0 then false
else {IPrime N Acc+1}
end
end
if N < 2 then false
else {IPrime N 2} end
end
end</syntaxhighlight>
=={{header|Panda}}==
In Panda you write a boolean function by making it filter, either returning it's input or nothing.
<syntaxhighlight lang="panda">fun prime(p) type integer->integer
p.gt(1) where q=p.sqrt NO(p.mod(2..q)==0)
1..100.prime</syntaxhighlight>
=={{header|PARI/GP}}==
<
if(n < 4, return(n > 1)); /* Handle negatives */
forprime(p=2,
if(n%p == 0, return(0))
);
1
};</
=={{header|Pascal}}==
{{trans|
<
function prime(n: integer): boolean;
Line 1,440 ⟶ 3,831:
if (prime(n)) then
write(n, ' ');
end.</
{{out}}
===improved using number wheel===
{{libheader|primTrial}}{{works with|Free Pascal}}
<syntaxhighlight lang="pascal">program TestTrialDiv;
{$IFDEF FPC}
{$MODE DELPHI}{$Smartlink ON}
{$ELSE}
{$APPLICATION CONSOLE}// for Delphi
{$ENDIF}
uses
primtrial;
{ Test and display primes 0 .. 50 }
begin
repeat
write(actPrime,' ');
until nextPrime > 50;
end.</syntaxhighlight>
;Output:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
=={{header|Perl}}==
A
<
$n % $_ or return for 2 .. sqrt $n;
$n > 1
}
print join(', ' => grep prime, 1..100), "\n";</
===Excluding multiples of 2 and 3===
One of many ways of writing trial division using a mod-6 wheel. Almost 2x faster than the simple method shown earlier.
<syntaxhighlight lang="perl">sub isprime {
my $n = shift;
return ($n >= 2) if $n < 4;
return unless $n % 2 && $n % 3;
my $sqrtn = int(sqrt($n));
for (my $i = 5; $i <= $sqrtn; $i += 6) {
return unless $n % $i && $n % ($i+2);
}
1;
}
my $s = 0;
$s += !!isprime($_) for 1..100000;
print "Pi(100,000) = $s\n";</syntaxhighlight>
===By Regular Expression===
JAPH by Abigail 1999 [http://diswww.mit.edu/bloom-picayune.mit.edu/perl/12606] in conference slides 2000 [http://www.perlmonks.org/?node_id=21580].
While this is extremely clever and often used for [[wp:Code golf|Code golf]], it should never be used for real work (it is extremely slow and uses lots of memory).
<syntaxhighlight lang="perl">sub isprime {
('1' x shift) !~ /^1?$|^(11+?)\1+$/
}
print join(', ', grep(isprime($_), 0..39)), "\n";</syntaxhighlight>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">is_prime_by_trial_division</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">32</span><span style="color: #0000FF;">),</span><span style="color: #000000;">is_prime_by_trial_division</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{2,3,5,7,11,13,17,19,23,29,31}
</pre>
=={{header|PHP}}==
<
function prime($a) {
if (($a % 2 == 0 && $a != 2) || $a < 2)
Line 1,493 ⟶ 3,922:
if (prime($x)) echo "$x\n";
?></
===By Regular Expression===
<
function prime($a) {
return !preg_match('/^1?$|^(11+?)\1+$/', str_repeat('1', $a));
}
?></
=={{header|Picat}}==
Here are four different versions.
===Iterative===
<syntaxhighlight lang="picat">is_prime1(N) =>
if N == 2 then
true
elseif N <= 1 ; N mod 2 == 0 then
false
else
foreach(I in 3..2..ceiling(sqrt(N)))
N mod I > 0
end
end.</syntaxhighlight>
===Recursive===
<syntaxhighlight lang="picat">is_prime2(N) =>
(N == 2 ; is_prime2b(N,3)).
is_prime2b(N,_Div), N <= 1 => false.
is_prime2b(2,_Div) => true.
is_prime2b(N,_Div), N mod 2 == 0 => false.
is_prime2b(N,Div), Div > ceiling(sqrt(N)) => true.
is_prime2b(N,Div), Div > 2 =>
(N mod Div == 0 ->
false
;
is_prime2b(N,Div+2)
).</syntaxhighlight>
===Functional===
<syntaxhighlight lang="picat">is_prime3(2) => true.
is_prime3(3) => true.
is_prime3(P) => P > 3, P mod 2 =\= 0, not has_factor3(P,3).
has_factor3(N,L), N mod L == 0 => true.
has_factor3(N,L) => L * L < N, L2 = L + 2, has_factor3(N,L2).</syntaxhighlight>
===Generator approach===
{{trans|Prolog}}
<code>prime2(N)</code> can be used to generate primes until memory is exhausted.
Difference from Prolog implementation: Picat does not support <code>between/3</code> with
"inf" as upper bound, so a high number (here 2**156+1) must be used.
<syntaxhighlight lang="picat">prime2(2).
prime2(N) :-
between(3, 2**156+1, N),
N mod 2 = 1, % odd
M is floor(sqrt(N+1)), % round-off paranoia
Max is (M-1) // 2, % integer division
foreach(I in 1..Max) N mod (2*I+1) > 0 end.</syntaxhighlight>
===Test===
<syntaxhighlight lang="picat">go =>
println([I : I in 1..100, is_prime1(I)]),
nl,
foreach(P in 1..6)
Primes = [ I : I in 1..10**P, is_prime1(I)],
println([10**P,Primes.len])
end,
nl.</syntaxhighlight>
{{out}}
<pre>[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
[10,4]
[100,25]
[1000,168]
[10000,1229]
[100000,9592]
[1000000,78498]</pre>
===Benchmark===
Times for calculating the number of primes below 10, 100,1_000,10_000, 100_000, and 1_000_000 respectively.
* imperative: <code>is_prime1/1</code> (0.971)
* recursive: <code>is_prime2/1</code> (3.258s)
* functional: <code>is_prime3/1</code> (0.938s)
* test/generate <code>prime2/1</code> (2.129s)
=={{header|PicoLisp}}==
<
(or
(= N 2)
Line 1,508 ⟶ 4,017:
(> N 1)
(bit? 1 N)
(
(
(T (
(T (=0 (% N D)) NIL) ) ) ) ) )</syntaxhighlight>
=={{header|PL/0}}==
The program waits for a number. Then it displays 1 if the number is prime, 0 otherwise.
<syntaxhighlight lang="pascal">
var p, isprime;
procedure checkprimality;
var i, isichecked;
begin
isprime := 0;
if p = 2 then isprime := 1;
if p >= 3 then
begin
i := 2; isichecked := 0;
while isichecked = 0 do
begin
if (p / i) * i = p then isichecked := 1;
if isichecked <> 1 then
if i * i >= p then
begin
isprime := 1; isichecked := 1
end;
i := i + 1
end
end
end;
begin
? p;
call checkprimality;
! isprime
end.
</syntaxhighlight>
4 runs:
{{in}}
<pre>1</pre>
{{out}}
<pre> 0</pre>
{{in}}
<pre>25</pre>
{{out}}
<pre> 0</pre>
{{in}}
<pre>43</pre>
{{out}}
<pre> 1</pre>
{{in}}
<pre>101</pre>
{{out}}
<pre> 1</pre>
=={{header|PL/I}}==
<
declare n fixed (15);
declare i fixed (10);
Line 1,525 ⟶ 4,085:
end;
return ('1'b);
end is_prime;</
=={{header|
This can be compiled with the original 8080 PL/M compiler and run under CP/M or an emulator or clone.
<br>Note that all integers in 8080 PL/M are unsigned.
<syntaxhighlight lang="pli">100H: /* TEST FOR PRIMALITY BY TRIAL DIVISION */
DECLARE FALSE LITERALLY '0', TRUE LITERALLY '0FFH';
/* CP/M BDOS SYSTEM CALL */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$STRING( .( 0DH, 0AH, '$' ) ); END;
PR$NUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
N$STR( W := LAST( N$STR ) ) = '$';
N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* INTEGER SUARE ROOT: BASED ON THE ONE IN THE PL/M FOR FROBENIUS NUMBERS */
SQRT: PROCEDURE( N )ADDRESS;
DECLARE ( N, X0, X1 ) ADDRESS;
IF N <= 3 THEN DO;
IF N = 0 THEN X0 = 0; ELSE X0 = 1;
END;
ELSE DO;
X0 = SHR( N, 1 );
DO WHILE( ( X1 := SHR( X0 + ( N / X0 ), 1 ) ) < X0 );
X0 = X1;
END;
END;
RETURN X0;
END SQRT;
IS$PRIME: PROCEDURE( N )BYTE; /* RETURNS TRUE IF N IS PRIME, FALSE IF NOT */
ELSE IF ( N AND 1 ) = 0 THEN RETURN N = 2;
ELSE DO;
/* ODD NUMBER > 2 */
DECLARE I ADDRESS;
DO I = 3 TO SQRT( N ) BY 2;
IF N MOD I = 0 THEN RETURN FALSE;
END;
RETURN TRUE;
END;
END IS$PRIME;
/* TEST THE IS$PRIME PROCEDURE */
DECLARE I ADDRESS;
DO I = 0 TO 100;
CALL PR$NUMBER( I );
END;
END;
CALL PR$NL;
EOF</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
</pre>
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function isPrime ($n) {
if ($n -eq 1) {$false}
elseif ($n -eq 2) {$true}
elseif ($n -eq 3) {$true}
else{
$m = [Math]::Floor([Math]::Sqrt($n))
(@(2..$m | where {($_ -lt $n) -and ($n % $_ -eq 0) }).Count -eq 0)
}
}
1..15 | foreach{"isPrime $_ : $(isPrime $_)"}</syntaxhighlight>
<b>Output:</b>
<pre>isPrime 1 : False
isPrime 2 : True
isPrime 3 : True
isPrime 4 : False
isPrime 5 : True
isPrime 6 : False
isPrime 7 : True
isPrime 8 : False
isPrime 9 : False
isPrime 10 : False
isPrime 11 : True
isPrime 12 : False
isPrime 13 : True
isPrime 14 : False
isPrime 15 : False</pre>
=={{header|Prolog}}==
The following predicate showcases Prolog's support for writing predicates suitable for both testing and generating. In this case, assuming the Prolog implemenation supports indefinitely large integers, prime(N) can be used to generate primes until memory is exhausted.
<syntaxhighlight lang="prolog">prime(2).
prime(N) :-
between(3, inf, N),
1 is N mod
M is floor(sqrt(N+1)), % round-off paranoia
Max is (M-1) // 2, % integer division
forall( between(1, Max, I), N mod (2*I+1) > 0 ).</syntaxhighlight>
Example using SWI-Prolog:
<pre>?- time( (bagof( P, (prime(P), ((P > 100000, !, fail); true)), Bag),
length(Bag,N),
last(Bag,Last),
writeln( (N,Last) ) )).
% 1,724,404 inferences, 1.072 CPU in 1.151 seconds (93% CPU, 1607873 Lips)
Bag = [2, 3, 5, 7, 11, 13, 17, 19, 23|...],
N = 9592,
Last = 99991.
?- time( prime(99991) ).
% 165 inferences, 0.000 CPU in 0.000 seconds (92% CPU, 1213235 Lips)
true.
?-</pre>
=={{header|Python}}==
The simplest primality test, using trial division:
{{works with|Python|2.5}}
<
return not (a < 2 or any(a % x == 0 for x in xrange(2, int(a**0.5) + 1)))</
Another test. Exclude even numbers first:
<
if a == 2: return True
if a < 2 or a % 2 == 0: return False
return not any(a % x == 0 for x in xrange(3, int(a**0.5) + 1, 2))</
Yet another test. Exclude multiples of 2 and 3, see http://www.devx.com/vb2themax/Tip/19051:
{{works with|Python|2.4}}
<
if a < 2: return False
if a == 2 or a == 3: return True # manually test 2 and 3
Line 1,600 ⟶ 4,232:
i = 6 - i # this modifies 2 into 4 and viceversa
return True</
===By Regular Expression===
Regular expression by "Abigail".<br>
(An explanation is given in "[http://paddy3118.blogspot.com/2009/08/story-of-regexp-and-primes.html The Story of the Regexp and the Primes]").
<
>>> def isprime(n):
return not re.match(r'^1?$|^(11+?)\1+$', '1' * n)
Line 1,610 ⟶ 4,242:
>>> # A quick test
>>> [i for i in range(40) if isprime(i)]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]</
=={{header|Qi}}==
<
K N -> true where (> (* K K) N)
K N -> false where (= 0 (MOD N K))
Line 1,622 ⟶ 4,254:
2 -> true
N -> false where (= 0 (MOD N 2))
N -> (prime?-0 3 N))</
=={{header|Quackery}}==
<code>sqrt+</code> is defined at [[Isqrt (integer square root) of X#Quackery]].
<syntaxhighlight lang="quackery"> [ dup 4 < iff [ 1 > ] done
dup 1 & not iff [ drop false ] done
true swap dup sqrt+
0 = iff [ 2drop not ] done
1 >> times
[ dup i^ 1 << 3 + mod 0 = if
[ dip not conclude ] ]
drop ] is isprime ( n --> b )
</syntaxhighlight>
=={{header|R}}==
<syntaxhighlight lang="rsplus">is.prime <- function(n) n == 2 || n > 2 && n %% 2 == 1 && (n < 9 || all(n %% seq(3, floor(sqrt(n)), 2) > 0))
# [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97</syntaxhighlight>
=={{header|Racket}}==
<
(define (prime? number)
Line 1,644 ⟶ 4,284:
((even? number) (= 2 number))
(else (for/and ((i (in-range 3 (ceiling (sqrt number)))))
(not (zero? (remainder number i)))))))</
=={{header|Raku}}==
(formerly Perl 6)
Here we use a "none" junction which will autothread through the <tt>%%</tt> "is divisible by" operator to assert that <tt>$i</tt> is not divisible by 2 or any of the numbers up to its square root. Read it just as you would English: "Integer <tt>$i</tt> is prime if it is greater than one and is divisible by none of 2, 3, up to the square root of <tt>$i</tt>."
<syntaxhighlight lang="raku" line>sub prime (Int $i --> Bool) {
$i > 1 and so $i %% none 2..$i.sqrt;
}</syntaxhighlight>
This can easily be improved in two ways. First, we generate the primes so we only divide by those, instead of all odd numbers. Second, we memoize the result using the <tt>//=</tt> idiom of Perl, which does the right-hand calculation and assigns it only if the left side is undefined. We avoid recalculating the square root each time. Note the mutual recursion that depends on the implicit laziness of list evaluation:
<syntaxhighlight lang="raku" line>my @primes = 2, 3, 5, -> $p { ($p+2, $p+4 ... &prime)[*-1] } ... *;
my @isprime = False,False; # 0 and 1 are not prime by definition
sub prime($i) {
my \limit = $i.sqrt.floor;
@isprime[$i] //= so ($i %% none @primes ...^ { $_ > limit })
}
say "$_ is{ "n't" x !prime($_) } prime." for 1 .. 100;</syntaxhighlight>
=={{header|REBOL}}==
<
case [
n = 2 [ true ]
Line 1,658 ⟶ 4,315:
]
]
]</
<
=={{header|REXX}}==
===compact version===
This version uses a technique which increments by six for testing primality (up to the
Programming note: all the REXX programs below show all primes up and including the number specified.
::: If the number is negative, the absolute value of it is used for the upper limit, but no primes are shown.
::: The ''number'' of primes found is always shown.
Also, it was determined that computing the (integer) square root of the number to be tested in the '''isPrime'''
<br>function slowed up the function (for all three REXX versions), however, for larger numbers of '''N''', it would
<br>be faster.
<syntaxhighlight lang="rexx">/*REXX program tests for primality by using (kinda smartish) trial division. */
parse arg n .; if n=='' then n=10000 /*let the user choose the upper limit. */
tell=(n>0); n=abs(n) /*display the primes only if N > 0. */
p=0 /*a count of the primes found (so far).*/
do j=-57 to n /*start in the cellar and work up. */
if \isPrime(j) then iterate /*if not prime, then keep looking. */
p=p+1 /*bump the jelly bean counter. */
if tell then say right(j,20) 'is prime.' /*maybe display prime to the terminal. */
end /*j*/
say
say
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: procedure; parse arg x /*get the number to be tested. */
if
do k=5 by 6 until k*k>x /*skips odd multiples of 3. */
end /*k*/ /*divide up through the √ x */
return 1 /*done dividing, it's prime. */</syntaxhighlight>
{{out|output|text= when using the default input of: <tt> 100 </tt>}}
<pre>
2 is prime.
3 is prime.
Line 1,717 ⟶ 4,379:
97 is prime.
===optimized version===
This version separates multiple-clause '''
<br>making it about 8% faster.
<
parse arg n .; if n=='' then
p=0 /*a count of the primes found (so far).
do j=-57 to n /*start in the cellar and work up. */
if \
p=p+1 /*bump the jelly bean counter. */
if
end /*j*/
say
say
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: procedure; parse arg x /*get integer to be investigated.*/
if x<11 then return wordpos(x, '2 3 5 7')\==0 /*is it a wee prime? */
if
if x//3==0 then return 0 /* ··· and eliminate the triples.*/
if x//
if x//(k+2)==0 then return 0 /* ··· and the next umpty one.
{{out|output|text= is identical to the first version when the same input is used.}}
===unrolled version===
This version uses an ''unrolled'' version (of the 2<sup>nd</sup> version) of some multiple-clause '''
<br>also an optimized version of the testing of low primes is used, making it about 22% faster.
<br><br>Note that the '''
<
parse arg n .; if n=='' then
p=0 /*a count of the primes found (so far).
do j=-57 to n /*start in the cellar and work up. */
if \
p=p+1 /*bump the jelly bean counter. */
if
end /*j*/
say
say "There are " p " primes up to " n ' (inclusive).'
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: procedure; parse arg x /*get the integer to be investigated. */
if x<107 then return wordpos(x, '2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53',
'59 61 67 71 73 79 83 89 97 101 103')\==0 /*some low primes.*/
if x// 2 ==0 then return 0 /*eliminate all the even numbers. */
if x// 3 ==0 then return 0 /* ··· and eliminate the triples. */
parse var x '' -1 _ /* obtain the rightmost digit.*/
if _ ==5 then return 0 /* ··· and eliminate the nickels. */
if x// 7 ==0 then return 0 /* ··· and eliminate the luckies. */
if x//11 ==0 then return 0
if x//13 ==0 then return 0
if x//17 ==0 then return 0
if x//19 ==0 then return 0
if x//23 ==0 then return 0
if x//29 ==0 then return 0
if x//31 ==0 then return 0
if x//37 ==0 then return 0
if x//41 ==0 then return 0
if x//43 ==0 then return 0
if x//47 ==0 then return 0
if x//53 ==0 then return 0
if x//59 ==0 then return 0
if x//61 ==0 then return 0
if x//67 ==0 then return 0
if x//71 ==0 then return 0
if x//73 ==0 then return 0
if x//79 ==0 then return 0
if x//83 ==0 then return 0
if x//89 ==0 then return 0
if x//97 ==0 then return 0
if x//101==0 then return 0
if x//103==0 then return 0 /*Note: REXX // is ÷ remainder. */
do k=107 by 6 while k*k<=x /*this skips odd multiples of three. */
if x//k ==0 then return 0 /*perform a divide (modulus), */
if x//(k+2)==0 then return 0 /* ··· and the next also. ___ */
end /*k*/ /*divide up through the √ x */
return 1 /*after all that, ··· it's a prime. */</syntaxhighlight>
{{out|output|text= is identical to the first version when the same input is used.}}<br><br>
=={{header|Ring}}==
<syntaxhighlight lang="ring">give n
flag = isPrime(n)
if flag = 1 see n + " is a prime number"
else see n + " is not a prime number" ok
func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i
next
return 1</syntaxhighlight>
=={{header|RPL}}==
{{trans|Python}}
This version use binary integers
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪ / LAST ROT * - #0 == ≫ '<span style="color:blue">BDIV?</span>' STO
≪
'''IF''' DUP #3 ≤ '''THEN''' #2 / B→R
'''ELSE'''
'''IF''' DUP #2 <span style="color:blue">BDIV?</span> OVER #3 '''BDIV?''' OR
'''WHILE''' 1 FS? OVER maxd ≤ AND '''REPEAT'''
'''IF''' a OVER <span style="color:blue">BDIV?</span> '''THEN''' 1 CF '''END'''
OVER + #6 ROT - SWAP '''END'''
SWAP DROP <span style="color:blue">BDIV?</span> NOT
'''END'''
≫ '<span style="color:blue">BPRIM?</span>' STO
|
<span style="color:blue">BDIV?</span> ''( #a #b -- boolean )''
<span style="color:blue">BPRIM?</span> ''( #a -- boolean )''
return 1 if
if 2 or 3 divides a
return 0
else
store a and root(a)
initialize stack with a i d and set flag 1 to control loop exit
while d <= root(a)
prepare loop exit if d divides a
i = 6 - i which modifies 2 into 4 and viceversa
empty stack and return result
|}
'''Floating point version'''
Faster but limited to 1E12.
≪ '''IF''' DUP 5 ≤ '''THEN''' { 2 3 5 } SWAP POS
'''ELSE'''
'''IF''' DUP 2 MOD NOT '''THEN''' 2
'''ELSE'''
DUP √ CEIL → lim
≪ 3 '''WHILE''' DUP2 MOD OVER lim ≤ AND '''REPEAT''' 2 + '''END'''
≫
'''END''' MOD
'''END''' SIGN
≫ '<span style="color:blue">PRIM?</span>' STO
=={{header|Ruby}}==
<
if a == 2
true
Line 1,821 ⟶ 4,545:
false
else
divisors =
divisors.none? { |d| a % d == 0 }
end
end
p (1..50).select{|i| prime(i)}</syntaxhighlight>
The '''prime''' package in the stdlib for Ruby contains this compact <code>Prime#prime?</code> method:
<syntaxhighlight lang="ruby">require "prime"
def prime?(value, generator = Prime::Generator23.new)
for num in generator
q,r = value.divmod num
return true if q < num
return false if r == 0
end
end
p (1..50).select{|i| prime?(i)}</syntaxhighlight>
Without any fancy stuff:
<
(enclose = lambda { |primes|
primes.last.succ.upto(limit) do |trial_pri|
if primes.
return enclose.call(primes << trial_pri)
end
Line 1,845 ⟶ 4,573:
primes
}).call([2])
end
p primes(50)</syntaxhighlight>
{{out}}
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
===By Regular Expression===
<
'1'*n !~ /^1?$|^(11+?)\1+$/
end</
===Prime Generators Tests===
Mathematicaly basis of Prime Generators
https://www.academia.edu/19786419/PRIMES-UTILS_HANDBOOK
https://www.academia.edu/42734410/Improved_Primality_Testing_and_Factorization_in_Ruby_revised
<syntaxhighlight lang="ruby">require "benchmark/ips"
# the simplest PG primality test using the P3 prime generator
# reduces the number space for primes to 2/6 (33.33%) of all integers
def primep3?(n) # P3 Prime Generator primality test
# P3 = 6*k + {5, 7} # P3 primes candidates (pc) sequence
return n | 1 == 3 if n < 5 # n: 0,1,4|false, 2,3|true
return false if n.gcd(6) != 1 # 1/3 (2/6) of integers are P3 pc
p, sqrtn = 5, Integer.sqrt(n) # first P3 sequence value
until p > sqrtn
return false if n % p == 0 || n % (p + 2) == 0 # if n is composite
p += 6 # first prime candidate for next kth residues group
end
true
end
# PG primality test using the P5 prime generator
# reduces the number space for primes to 8/30 (26.67%) of all integers
def primep5?(n) # P5 Prime Generator primality test
# P5 = 30*k + {7,11,13,17,19,23,29,31} # P5 primes candidates sequence
return [2, 3, 5].include?(n) if n < 7 # for small and negative values
return false if n.gcd(30) != 1 # 4/15 (8/30) of integers are P5 pc
p, sqrtn = 7, Integer.sqrt(n) # first P5 sequence value
until p > sqrtn
return false if # if n is composite
n % (p) == 0 || n % (p+4) == 0 || n % (p+6) == 0 || n % (p+10) == 0 ||
n % (p+12) == 0 || n % (p+16) == 0 || n % (p+22) == 0 || n % (p+24) == 0
p += 30 # first prime candidate for next kth residues group
end
true
end
# PG primality test using the P7 prime generator
# reduces the number space for primes to 48/210 (22.86%) of all integers
def primep7?(n)
# P7 = 210*k + {11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
# 89,97,101,103,107,109,113,121,127,131,137,139,143,149,151,157,163,
# 167,169,173,179,181,187,191,193,197,199,209,211}
return [2, 3, 5, 7].include?(n) if n < 11
return false if n.gcd(210) != 1 # 8/35 (48/210) of integers are P7 pc
p, sqrtn = 11, Integer.sqrt(n) # first P7 sequence value
until p > sqrtn
return false if
n % (p) == 0 || n % (p+2) == 0 || n % (p+6) == 0 || n % (p+8) == 0 ||
n % (p+12) == 0 || n % (p+18) == 0 || n % (p+20) == 0 || n % (p+26) == 0 ||
n % (p+30) == 0 || n % (p+32) == 0 || n % (p+36) == 0 || n % (p+42) == 0 ||
n % (p+48) == 0 || n % (p+50) == 0 || n % (p+56) == 0 || n % (p+60) == 0 ||
n % (p+62) == 0 || n % (p+68) == 0 || n % (p+72) == 0 || n % (p+78) == 0 ||
n % (p+86) == 0 || n % (p+90) == 0 || n % (p+92) == 0 || n % (p+96) == 0 ||
n % (p+98) == 0 || n % (p+102) == 0 || n % (p+110) == 0 || n % (p+116) == 0 ||
n % (p+120) == 0 || n % (p+126) == 0 || n % (p+128) == 0 || n % (p+132) == 0 ||
n % (p+138) == 0 || n % (p+140) == 0 || n % (p+146) == 0 || n % (p+152) == 0 ||
n % (p+156) == 0 || n % (p+158) == 0 || n % (p+162) == 0 || n % (p+168) == 0 ||
n % (p+170) == 0 || n % (p+176) == 0 || n % (p+180) == 0 || n % (p+182) == 0 ||
n % (p+186) == 0 || n % (p+188) == 0 || n % (p+198) == 0 || n % (p+200) == 0
p += 210 # first prime candidate for next kth residues group
end
true
end
# Benchmarks to test for various size primes
p = 541
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
b.compare!
puts
end
p = 1000003
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
b.compare!
puts
end
p = 4294967291 # largest prime < 2**32
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
b.compare!
puts
end
p = (10 ** 16) * 2 + 3
Benchmark.ips do |b|
print "\np = #{p}"
b.report("primep3?") { primep3?(p) }
b.report("primep5?") { primep5?(p) }
b.report("primep7?") { primep7?(p) }
b.compare!
puts
end</syntaxhighlight>
{{out}}
<pre>p = 541
Warming up --------------------------------------
primep3? 109.893k i/100ms
primep5? 123.949k i/100ms
primep7? 44.216k i/100ms
Calculating -------------------------------------
primep3? 1.598M (± 3.4%) i/s - 8.022M in 5.025036s
primep5? 1.872M (± 6.3%) i/s - 9.420M in 5.059896s
primep7? 502.040k (± 1.2%) i/s - 2.520M in 5.020919s
Comparison:
primep5?: 1871959.0 i/s
primep3?: 1598489.8 i/s - 1.17x slower
primep7?: 502039.8 i/s - 3.73x slower
p = 1000003
Warming up --------------------------------------
primep3? 5.850k i/100ms
primep5? 9.013k i/100ms
primep7? 10.889k i/100ms
Calculating -------------------------------------
primep3? 59.965k (± 1.1%) i/s - 304.200k in 5.073641s
primep5? 92.561k (± 2.1%) i/s - 468.676k in 5.065709s
primep7? 109.335k (± 0.8%) i/s - 555.339k in 5.079549s
Comparison:
primep7?: 109334.7 i/s
primep5?: 92561.4 i/s - 1.18x slower
primep3?: 59964.5 i/s - 1.82x slower
p = 4294967291
Warming up --------------------------------------
primep3? 92.000 i/100ms
primep5? 148.000 i/100ms
primep7? 184.000 i/100ms
Calculating -------------------------------------
primep3? 926.647 (± 1.1%) i/s - 4.692k in 5.064067s
primep5? 1.480k (± 1.7%) i/s - 7.400k in 5.001399s
primep7? 1.804k (± 1.0%) i/s - 9.200k in 5.099110s
Comparison:
primep7?: 1804.4 i/s
primep5?: 1480.0 i/s - 1.22x slower
primep3?: 926.6 i/s - 1.95x slower
p = 20000000000000003
Warming up --------------------------------------
primep3? 1.000 i/100ms
primep5? 1.000 i/100ms
primep7? 1.000 i/100ms
Calculating -------------------------------------
primep3? 0.422 (± 0.0%) i/s - 3.000 in 7.115929s
primep5? 0.671 (± 0.0%) i/s - 4.000 in 5.957077s
primep7? 0.832 (± 0.0%) i/s - 5.000 in 6.007834s
Comparison:
primep7?: 0.8 i/s
primep5?: 0.7 i/s - 1.24x slower
primep3?: 0.4 i/s - 1.97x slower
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">fn is_prime(n: u64) -> bool {
match n {
0 | 1 => false,
2 => true,
_even if n % 2 == 0 => false,
_ => {
let sqrt_limit = (n as f64).sqrt() as u64;
(3..=sqrt_limit).step_by(2).find(|i| n % i == 0).is_none()
}
}
}
fn main() {
for i in (1..30).filter(|i| is_prime(*i)) {
println!("{} ", i);
}
}</syntaxhighlight>
{{out}}
<pre>2 3 5 7 11 13 17 19 23 29 </pre>
=={{header|S-lang}}==
<syntaxhighlight lang="s-lang">define is_prime(n)
{
if (n == 2) return(1);
if (n <= 1) return(0);
if ((n & 1) == 0) return(0);
variable mx = int(sqrt(n)), i;
_for i (3, mx, 1) {
if ((n mod i) == 0)
return(0);
}
return(1);
}
define ptest()
{
variable lst = {};
_for $1 (1, 64, 1)
if (is_prime($1))
list_append(lst, string($1));
print(strjoin(list_to_array(lst), ", "));
}
ptest();</syntaxhighlight>
{{out}}
"2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61"
=={{header|SAS}}==
<
do n=1 to 1000;
link primep;
Line 1,889 ⟶ 4,829:
return;
keep n;
run;</
=={{header|Scala}}==
===Simple version===
<syntaxhighlight lang="scala"> def isPrime(n: Int) =
n > 1 && (Iterator.from(2) takeWhile (d => d * d <= n) forall (n % _ != 0))</syntaxhighlight>
===Accelerated version [[functional_programming|FP]] and parallel runabled===
// {{Out}}Best seen running in your browser [https://scastie.scala-lang.org/1RLimJrRQUqkXWkUwUxgYg Scastie (remote JVM)].
<syntaxhighlight lang="scala">object IsPrimeTrialDivision extends App {
def isPrime(n: Long) =
n > 1 && ((n & 1) != 0 || n == 2) && (n % 3 != 0 || n == 3) &&
(5 to math.sqrt(n).toInt by 6).par.forall(d => n % d != 0 && n % (d + 2) != 0)
assert(!isPrime(
assert(!isPrime(
assert(isPrime(2))
assert(isPrime(100000000019L))
assert(isPrime(100000000057L))
assert(isPrime(100000000063L))
assert(isPrime(100000000069L))
assert(isPrime(100000000073L))
assert(isPrime(100000000091L))
println("10 Numbers tested. A moment please …\nNumber crunching biggest 63-bit prime …")
assert(isPrime(9223372036854775783L)) // Biggest 63-bit prime
println("All done")
}</syntaxhighlight>
===Accelerated version [[functional_programming|FP]], tail recursion===
Tests 1.3 M numbers against OEIS prime numbers.
<syntaxhighlight lang="scala">import scala.annotation.tailrec
import scala.io.Source
object PrimesTestery extends App {
val rawText = Source.fromURL("https://oeis.org/A000040/a000040.txt")
val oeisPrimes = rawText.getLines().take(100000).map(_.split(" ")(1)).toVector
def isPrime(n: Long) = {
@tailrec
def inner(d: Int, end: Int): Boolean = {
if (d > end) true
else if (n % d != 0 && n % (d + 2) != 0) inner(d + 6, end) else false
}
n > 1 && ((n & 1) != 0 || n == 2) &&
(n % 3 != 0 || n == 3) && inner(5, math.sqrt(n).toInt)
}
println(oeisPrimes.size)
for (i <- 0 to 1299709) assert(
}</syntaxhighlight>
=={{header|Scheme}}==
{{Works with|Scheme|R<math>^5</math>RS}}
<
(define (*prime? divisor)
(or (> (* divisor divisor) number)
Line 1,918 ⟶ 4,890:
(*prime? (+ divisor 1)))))
(and (> number 1)
(*prime? 2)))</
<
(define (prime? n)
(if (< n 4) (> n 1)
Line 1,927 ⟶ 4,899:
(or (> (* k k) n)
(and (positive? (remainder n k))
(loop (+ k 2))))))))</
=={{header|Seed7}}==
<
result
var boolean: prime is FALSE;
Line 1,939 ⟶ 4,911:
if number = 2 then
prime := TRUE;
elsif odd(number)
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
Line 1,948 ⟶ 4,918:
prime := testNum > upTo;
end if;
end func;</
Original source: [http://seed7.sourceforge.net/algorith/math.htm#is_prime]
=={{header|SETL}}==
<syntaxhighlight lang="setl">program trial_division;
print({n : n in {1..100} | prime n});
op prime(n);
return n>=2 and not exists d in {2..floor sqrt n} | n mod d = 0;
end op;
end program;</syntaxhighlight>
{{out}}
<pre>{2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97}</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func is_prime(a) {
given (a) {
when (2) { true }
case (a <= 1 || a.is_even) { false }
default { 3 .. a.isqrt -> any { .divides(a) } -> not }
}
}</syntaxhighlight>
{{trans|Perl}}
Alternative version, excluding multiples of 2 and 3:
<syntaxhighlight lang="ruby">func is_prime(n) {
return (n >= 2) if (n < 4)
return false if (n%%2 || n%%3)
for k in (5 .. n.isqrt -> by(6)) {
return false if (n%%k || n%%(k+2))
}
return true
}</syntaxhighlight>
=={{header|Smalltalk}}==
<syntaxhighlight lang="smalltalk">| isPrime |
isPrime := [:n |
n even ifTrue: [ ^n=2 ]
ifFalse: [
3 to: n sqrt do: [:i |
(n \\ i = 0) ifTrue: [ ^false ]
].
^true
]
]</syntaxhighlight>
=={{header|SNOBOL4}}==
<
isprime isprime = n
le(n,1) :s(freturn)
Line 1,960 ⟶ 4,971:
isp1 i = le(i + 2,max) i + 2 :f(return)
eq(remdr(n,i),0) :s(freturn)f(isp1)
isprime_end</
===By Patterns===
Using the Abigail regex transated to Snobol patterns.
<
rprime str = dupl('1',n); rprime = n
pat1 = ('1' | '')
Line 1,974 ⟶ 4,985:
n = lt(n,50) n + 1 :s(loop)
output = rprimes
end</
{{out}}
=={{header|SparForte}}==
As a structured script.
<syntaxhighlight lang="ada">#!/usr/local/bin/spar
pragma annotate( summary, "prime" );
pragma annotate( description, "Write a boolean function that tells whether a given" );
pragma annotate( description, "integer is prime. Remember that 1 and all" );
pragma annotate( description, "non-positive numbers are not prime. " );
pragma annotate( see_also, "http://rosettacode.org/wiki/Primality_by_trial_division" );
pragma annotate( author, "Ken O. Burtch" );
pragma license( unrestricted );
pragma restriction( no_external_commands );
procedure prime is
function is_prime(item : positive) return boolean is
result : boolean := true;
test : natural;
begin
if item /= 2 and item mod 2 = 0 then
result := false;
else
test := 3;
while test < natural( numerics.sqrt( item ) ) loop
if natural(item) mod test = 0 then
result := false;
exit;
end if;
test := @ + 2;
end loop;
end if;
return result;
end is_prime;
number : positive;
result : boolean;
begin
number := 6;
result := is_prime( number );
put( number ) @ ( " : " ) @ ( result );
new_line;
number := 7;
result := is_prime( number );
put( number ) @ ( " : " ) @ ( result );
new_line;
number := 8;
result := is_prime( number );
put( number ) @ ( " : " ) @ ( result );
new_line;
end prime;</syntaxhighlight>
=={{header|SQL}}==
{{works with|T-SQL}}
<syntaxhighlight lang="tsql">declare @number int
set @number = 514229 -- number to check
Line 2,009 ⟶ 5,073:
' is prime'
end primalityTest
option (maxrecursion 0)</syntaxhighlight>
=={{header|Standard ML}}==
<
if n = 2 then true
else if n < 2 orelse n mod 2 = 0 then false
Line 2,022 ⟶ 5,085:
else loop (k+2)
in loop 3
end</
=={{header|Swift}}==
<syntaxhighlight lang="swift">import Foundation
extension Int {
func isPrime() -> Bool {
switch self {
case let x where x < 2:
return false
case 2:
return true
default:
return
self % 2 != 0 &&
!stride(from: 3, through: Int(sqrt(Double(self))), by: 2).contains {self % $0 == 0}
}
}
}</syntaxhighlight>
A version that works with Swift 5.x and probably later. Does not need to import Foundation
<syntaxhighlight lang="swift">
extension Int
{
func isPrime() -> Bool
{
if self < 3
{
return self == 2
}
else
{
let upperLimit = Int(Double(self).squareRoot())
return !self.isMultiple(of: 2) && !stride(from: 3, through: upperLimit, by: 2)
.contains(where: { factor in self.isMultiple(of: factor) })
}
}
}
</syntaxhighlight>
=={{header|Tcl}}==
<
if {$n <= 1} {return false}
if {$n == 2} {return true}
Line 2,033 ⟶ 5,136:
}
return true
}</
=={{header|UNIX Shell}}==
Line 2,068 ⟶ 5,144:
{{works with|pdksh}}
{{works with|zsh}}
<
typeset n=$1 p=3
(( n == 2 )) && return 0 # 2 is prime.
Line 2,082 ⟶ 5,158:
done
return 0 # Yes, n is prime.
}</
{{works with|Bourne Shell}}
<
set -- "$1" 3
test "$1" -eq 2 && return 0 # 2 is prime.
Line 2,098 ⟶ 5,174:
done
return 0 # Yes, n is prime.
}</
=={{header|Ursala}}==
Excludes even numbers, and loops only up to the approximate square root or until a factor is found.
<
#import nat
prime = ~<{0,1}&& -={2,3}!| ~&h&& (all remainder)^Dtt/~& iota@K31</
Test program to try it on a few numbers:
<
test = prime* <5,6,7></
{{out}}
<true,false,true>
=={{header|V}}==
{{trans|Joy}}
<
2
[[dup * >] [true] [false] ifte [% 0 >] dip and]
[succ]
while
dup * <].</
{{out|Using it}}
<
=true
|4 prime?
=false</
=={{header|Verilog}}==
<syntaxhighlight lang="Verilog">module main;
integer i, k;
initial begin
$display("Prime numbers between 0 and 100:");
for(i = 2; i <= 99; i=i+1) begin
k=i;
if(i[0] != 1'b0) begin
if(k==3 | k==5 | k==7 | k==11 | k==13 | k==17 | k==19) $write(i);
else if(k%3==0 | k%5==0 | k%7==0 | k%11==0 | k%13==0 | k%17==0 | k%19==0) $write("");
else $write(i);
end
if(i==10'b00 | i==10'b010) $write(i);
end
$finish;
end
endmodule</syntaxhighlight>
=={{header|V (Vlang)}}==
<syntaxhighlight lang="Zig">
import math
const numbers = [5, 3, 14, 19, 25, 59, 88]
fn main() {
for num in numbers {
println("${num} is a prime number? " + if is_prime(num) == true {'yes'} else {'no'})
}
}
fn is_prime(num int) bool {
if num <= 1 {return false}
if num % 2 == 0 && num != 2 {return false}
for idx := 3; idx <= math.floor(num / 2) - 1; idx += 2 {
if num % idx == 0 {return false}
}
return true
}
</syntaxhighlight>
{{out}}
<pre>
5 is a prime number? yes
3 is a prime number? yes
14 is a prime number? no
19 is a prime number? yes
25 is a prime number? no
59 is a prime number? yes
88 is a prime number? no
</pre>
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./fmt" for Fmt
var isPrime = Fn.new { |n|
if (n < 2) return false
if (n%2 == 0) return n == 2
var p = 3
while (p * p <= n) {
if (n%p == 0) return false
p = p + 2
}
return true
}
var tests = [2, 5, 12, 19, 57, 61, 97]
System.print("Are the following prime?")
for (test in tests) {
Fmt.print("$2d -> $y", test, isPrime.call(test))
}</syntaxhighlight>
{{out}}
<pre>
Are the following prime?
2 -> yes
5 -> yes
12 -> no
19 -> yes
57 -> no
61 -> yes
97 -> yes
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">func Prime(N); \Return 'true' if N is a prime number
int N;
int I;
[if N <= 1 then return false;
for I:=
if rem(N/I) = 0 then return false;
return true;
];
int Num;
Line 2,145 ⟶ 5,302:
Text(0, if Prime(Num) then "is " else "not ");
Text(0, "prime^M^J");
until Num = 0</
{{out}}
<pre>777777777
not prime
777777773
is prime
0
not prime</pre>
=={{header|zkl}}==
The Method filter1 stops at the first non False result, which, if there is one, is the first found diviser, thus short cutting the rest of the test
<syntaxhighlight lang="zkl">fcn isPrime(n){
if(n.isEven or n<2) return(n==2);
(not [3..n.toFloat().sqrt().toInt(),2].filter1('wrap(m){n%m==0}))
}</syntaxhighlight>
{{out}}
<pre>zkl: [1..].filter(20,isPrime)
L(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71)
zkl: isPrime(777777773)
True
zkl: isPrime(777777777)
False</pre>
| |||