10001th prime
10001th prime is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
Find and show on this page the 10001st prime number.
11l
V k = 10001
V n = k * 17
V primes = [1B] * n
primes[0] = primes[1] = 0B
L(i) 2 .. Int(sqrt(n))
I !primes[i]
L.continue
L(j) (i * i .< n).step(i)
primes[j] = 0B
L(i) 0 .< n
I primes[i]
I k == 1
print(i)
L.break
k--- Output:
104743
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program prime1000164.s */
/************************************/
/* Constantes */
/************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
/************************************/
/* Macros */
/************************************/
//.include "../../ficmacros64.inc" // use for developper debugging
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessStartPgm: .asciz "Program 64 bits start \n"
szMessEndPgm: .asciz "Program normal end.\n"
szMessErrorArea: .asciz "\033[31mError : area divisors too small.\n"
szMessPrime: .asciz "Prime N0 10001 : "
szMessOverflow: .asciz "Overflow function isPrime.\n"
szCarriageReturn: .asciz "\n"
.align 4
qGraine: .quad 123456
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
.align 4
sZoneConv: .skip 24
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main: // program start
ldr x0,qAdrszMessStartPgm // display start message
bl affichageMess
mov x4,#1 // start number
mov x5,#1 // prime counter
ldr x2,iLimit
tst x4,#1
cinc x4,x4,eq // start with odd number
1:
mov x0,x4
bl isPrimeMiller // test miller rabin
cmp x0,#0
cinc x4,x4,eq
cinc x4,x4,eq
beq 1b
add x5,x5,#1
cmp x5,x2 // counter ok ?
cinc x4,x4,ne
cinc x4,x4,ne
bne 1b
ldr x0,qAdrszMessPrime
bl affichageMess
mov x0,x4
ldr x1,qAdrsZoneConv
bl conversion10 // decimal conversion
ldr x0,qAdrsZoneConv
bl affichageMess
ldr x0,qAdrszCarriageReturn
bl affichageMess
ldr x0,qAdrszMessEndPgm // display end message
bl affichageMess
100: // standard end of the program
mov x0, #0 // return code
mov x8,EXIT
svc 0 // perform system call
qAdrszMessStartPgm: .quad szMessStartPgm
qAdrszMessEndPgm: .quad szMessEndPgm
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsZoneConv: .quad sZoneConv
qAdrszMessPrime: .quad szMessPrime
iLimit: .quad 10001
/***************************************************/
/* check if a number is prime test miller rabin */
/***************************************************/
/* r0 contains the number */
/* r0 return 1 if prime 0 else */
//2147483647
//4294967297
//131071
isPrimeMiller:
stp x1,lr,[sp,-16]!
cmp x0,#1 // control 0 or 1
csel x0,xzr,x0,ls
bls 100f
cmp x0,#2 // control = 2
mov x1,1
csel x0,x1,x0,eq
beq 100f
tst x0,#1
csel x0,xzr,x0,eq // even
beq 100f
mov x1,#5 // loop number
bl testMiller
100:
ldp x1,lr,[sp],16
ret
/***************************************************/
/* test miller rabin algorithme wikipedia */
/* unsigned */
/***************************************************/
/* x0 contains number */
/* x1 contains parameter */
/* x0 return 1 if prime 0 if composite */
testMiller:
stp x1,lr,[sp,-16]! // TODO: save à completer
stp x2,x3,[sp,-16]!
stp x4,x5,[sp,-16]!
stp x6,x7,[sp,-16]!
stp x8,x9,[sp,-16]!
stp x10,x11,[sp,-16]!
mov x4,x0 // N
mov x7,x1 // loop maxi
sub x10,x0,#1 // D
mov x2,#2
mov x6,#0 // S
1: // compute D * 2 power S
lsr x10,x10,#1 // D= D/2
add x6,x6,#1 // increment S
tst x10,#1 // D even ?
beq 1b
2:
mov x8,#0 // loop counter
sub x5,x0,#3
3:
mov x0,x5
bl genereraleas
add x0,x0,#2 // alea (entre 2 et n-1)
mov x1,x10 // exposant = D
mov x2,x4 // modulo N
bl moduloPur64
cmp x0,#1
beq 5f
sub x1,x4,#1 // n -1
cmp x0,x1
beq 5f
sub x9,x6,#1 // S - 1
4:
mov x2,x0
mul x0,x2,x2 // compute square lower
umulh x1,x2,x2 // compute square upper
mov x2,x4 // and compute modulo N
bl divisionReg128U
mov x0,x3
cmp x0,#1
csel x0,xzr,x0,eq // composite
beq 100f
sub x1,x4,#1 // n -1
cmp x0,x1
beq 5f
subs x9,x9,#1
bge 4b
mov x0,#0 // composite
b 100f
5:
add x8,x8,#1
cmp x8,x7
blt 3b
mov x0,#1 // prime
100:
ldp x10,x11,[sp],16
ldp x8,x9,[sp],16
ldp x6,x7,[sp],16
ldp x4,x5,[sp],16
ldp x2,x3,[sp],16
ldp x1,lr,[sp],16 // TODO: retaur à completer
ret
/********************************************************/
/* Calcul modulo de b puissance e modulo m */
/* Exemple 4 puissance 13 modulo 497 = 445 */
/********************************************************/
/* x0 nombre */
/* x1 exposant */
/* x2 modulo */
moduloPur64:
stp x1,lr,[sp,-16]! // save registres
stp x3,x4,[sp,-16]! // save registres
stp x5,x6,[sp,-16]! // save registres
stp x7,x8,[sp,-16]! // save registres
stp x9,x10,[sp,-16]! // save registres
cbz x0,100f
cbz x1,100f
mov x8,x0
mov x7,x1
mov x6,1 // resultat
udiv x4,x8,x2
msub x9,x4,x2,x8 // contient le reste
1:
tst x7,1
beq 2f
mul x4,x9,x6
umulh x5,x9,x6
mov x6,x4
mov x0,x6
mov x1,x5
bl divisionReg128U
mov x6,x3
2:
mul x8,x9,x9
umulh x5,x9,x9
mov x0,x8
mov x1,x5
bl divisionReg128U
mov x9,x3
lsr x7,x7,1
cbnz x7,1b
mov x0,x6 // result
cmn x0,0 // carry à zero pas d'erreur
b 100f
99:
ldr x0,qAdrszMessOverflow
bl affichageMess
cmp x0,0 // carry à un car erreur
mov x0,-1 // code erreur
100:
ldp x9,x10,[sp],16 // restaur des 2 registres
ldp x7,x8,[sp],16 // restaur des 2 registres
ldp x5,x6,[sp],16 // restaur des 2 registres
ldp x3,x4,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret // retour adresse lr x30
qAdrszMessOverflow: .quad szMessOverflow
/***************************************************/
/* division d un nombre de 128 bits par un nombre de 64 bits */
/***************************************************/
/* x0 contient partie basse dividende */
/* x1 contient partie haute dividente */
/* x2 contient le diviseur */
/* x0 retourne partie basse quotient */
/* x1 retourne partie haute quotient */
/* x3 retourne le reste */
divisionReg128U:
stp x6,lr,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
mov x5,#0 // raz du reste R
mov x3,#128 // compteur de boucle
mov x4,#0 // dernier bit
1:
lsl x5,x5,#1 // on decale le reste de 1
tst x1,1<<63 // test du bit le plus à gauche
lsl x1,x1,#1 // on decale la partie haute du quotient de 1
beq 2f
orr x5,x5,#1 // et on le pousse dans le reste R
2:
tst x0,1<<63
lsl x0,x0,#1 // puis on decale la partie basse
beq 3f
orr x1,x1,#1 // et on pousse le bit de gauche dans la partie haute
3:
orr x0,x0,x4 // position du dernier bit du quotient
mov x4,#0 // raz du bit
cmp x5,x2
blt 4f
sub x5,x5,x2 // on enleve le diviseur du reste
mov x4,#1 // dernier bit à 1
4:
// et boucle
subs x3,x3,#1
bgt 1b
lsl x1,x1,#1 // on decale le quotient de 1
tst x0,1<<63
lsl x0,x0,#1 // puis on decale la partie basse
beq 5f
orr x1,x1,#1
5:
orr x0,x0,x4 // position du dernier bit du quotient
mov x3,x5
100:
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x6,lr,[sp],16 // restaur des 2 registres
ret // retour adresse lr x30
/***************************************************/
/* Generation random number */
/***************************************************/
/* x0 contains limit */
genereraleas:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
ldr x1,qAdrqGraine
ldr x2,[x1]
ldr x3,qNbDep1
mul x2,x3,x2
ldr x3,qNbDep2
add x2,x2,x3
str x2,[x1] // maj de la graine pour l appel suivant
cmp x0,#0
beq 100f
udiv x3,x2,x0
msub x0,x3,x0,x2 // résult = remainder
100: // end function
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrqGraine: .quad qGraine
qNbDep1: .quad 0x0019660d
qNbDep2: .quad 0x3c6ef35f
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeARM64.inc"- Output:
Program 64 bits start Prime N0 10001 : 104743 Program normal end.
Ada
-- Rosetta Code Task written in Ada
-- 10001th prime
-- https://rosettacode.org/wiki/10001th_prime
-- November 2024, R. B. E.
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
procedure Ten_Thousand_One_Prime is
function Is_Prime (N : in Natural) return Boolean is
Temp : Natural := 5;
begin
if N < 2 then
return False;
end if;
if N mod 2 = 0 then
return N = 2;
end if;
if N mod 3 = 00 then
return N = 3;
end if;
while Temp * Temp <= N loop
if N mod Temp = 0 then
return False;
end if;
Temp := Temp + 2;
if N mod Temp = 0 then
return False;
end if;
end loop;
return True;
end Is_Prime;
Nth_Prime : constant Positive := 10_001;
Prime_Counter : Natural := 0;
Prime_Candidate : Positive := 2;
begin
loop
if Is_Prime (Prime_Candidate) then
Prime_Counter := Prime_Counter + 1;
end if;
exit when Prime_Counter = Nth_Prime;
if Prime_Candidate = 2 then
Prime_Candidate := Prime_Candidate + 1;
else
Prime_Candidate := Prime_Candidate + 2;
end if;
end loop;
Put ("The ");
Put (Nth_Prime, 0);
Put ("th Prime is ");
Put (Prime_Candidate, 0);
New_Line;
end Ten_Thousand_One_Prime;
- Output:
The 10001th Prime is 104743
ALGOL 68
Chebyshev showed that the limit of pi( n ) / ( n / ln(n) ) as n approaches infinity is 1 ( pi( n ) is the number of primes up to n ).
The APPROXIMATESIEVESIZEFOR operator uses this to find a rough value for size of sieve needed to contain the required number of primes.
BEGIN # find the 10001st prime #
PR read "primes.incl.a68" PR
# construct a sieve of primes that should be large enough to contain 10001 primes #
INT required prime = 10 001;
[]BOOL prime = PRIMESIEVE APPROXIMATESIEVESIZEFOR required prime;
INT p count := 1;
FOR n FROM 3 BY 2 WHILE p count < required prime DO
IF prime[ n ] THEN
p count +:= 1;
IF p count = required prime THEN
print( ( "Prime ", whole( required prime, 0 ), " is ", whole( n, 0 ) ) )
FI
FI
OD
END- Output:
Prime 10001 is 104743
ARM Assembly
/* ARM assembly Raspberry PI */
/* program prime10001.s */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
/************************************/
/* Macros */
/************************************/
//.include "../../ficmacros32.inc" @ use for developper debugging
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessStartPgm: .asciz "Program 32 bits start \n"
szMessEndPgm: .asciz "Program normal end.\n"
szMessErrorArea: .asciz "\033[31mError : area divisors too small.\n"
szMessPrime: .asciz "Prime N0 10001 : "
szCarriageReturn: .asciz "\n"
.align 4
iGraine: .int 123456
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
.align 4
sZoneConv: .skip 24
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main: @ program start
ldr r0,iAdrszMessStartPgm @ display start message
bl affichageMess
mov r4,#1 @ start number
mov r5,#1 @ prime counter
ldr r2,iLimit
tst r4,#1
addeq r4,#1 @ start with odd number
1:
mov r0,r4
bl isPrimeMiller @ test miller rabin
cmp r0,#0
addeq r4,r4,#2
beq 1b
add r5,r5,#1
cmp r5,r2 @ counter ok ?
addne r4,r4,#2
bne 1b
ldr r0,iAdrszMessPrime
bl affichageMess
mov r0,r4
ldr r1,iAdrsZoneConv
bl conversion10 @ decimal conversion
ldr r0,iAdrsZoneConv
bl affichageMess
ldr r0,iAdrszCarriageReturn
bl affichageMess
ldr r0,iAdrszMessEndPgm @ display end message
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc 0 @ perform system call
iAdrszMessStartPgm: .int szMessStartPgm
iAdrszMessEndPgm: .int szMessEndPgm
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsZoneConv: .int sZoneConv
iAdrszMessPrime: .int szMessPrime
iLimit: .int 10001
/***************************************************/
/* check if a number is prime test miller rabin */
/***************************************************/
/* r0 contains the number */
/* r0 return 1 if prime 0 else */
@2147483647
@4294967297
@131071
isPrimeMiller:
push {r1-r6,lr} @ save registers
cmp r0,#1 @ control 0 or 1
movls r0,#0
bls 100f
cmp r0,#2 @ control = 2
moveq r0,#1
beq 100f
tst r0,#1
moveq r0,#0 @ even
beq 100f
mov r1,#5 @ loop number
bl testMiller
100:
pop {r1-r6,pc}
/***************************************************/
/* test miller rabin algorithme wikipedia */
/* unsigned */
/***************************************************/
/* r0 contains number */
/* r1 contains parameter */
/* r0 return 1 if prime 0 if composite */
testMiller:
push {r1-r9,lr} @ save registers
mov r4,r0 @ N
mov r7,r1 @ loop maxi
sub r3,r0,#1 @ D
mov r2,#2
mov r6,#0 @ S
1: @ compute D * 2 power S
lsr r3,#1 @ D= D/2
add r6,r6,#1 @ increment S
tst r3,#1 @ D even ?
beq 1b
2:
mov r8,#0 @ loop counter
sub r5,r0,#3
3:
mov r0,r5
bl genereraleas
add r0,r0,#2 @ alea (entre 2 et n-1)
mov r1,r3 @ exposant = D
mov r2,r4 @ modulo N
bl moduloPuR32
cmp r0,#1
beq 5f
sub r1,r4,#1 @ n -1
cmp r0,r1
beq 5f
sub r9,r6,#1 @ S - 1
4:
mov r2,r0
umull r0,r1,r2,r0 @ compute square
mov r2,r4 @ and compute modulo N
bl division32R2023
mov r0,r2
cmp r0,#1
moveq r0,#0 @ composite
beq 100f
sub r1,r4,#1 @ n -1
cmp r0,r1
beq 5f
subs r9,r9,#1
bge 4b
mov r0,#0 @ composite
b 100f
5:
add r8,r8,#1
cmp r8,r7
blt 3b
mov r0,#1 @ prime
100:
pop {r1-r9,pc}
/********************************************************/
/* Calcul modulo de b puissance e modulo m */
/* Exemple 4 puissance 13 modulo 497 = 445 */
/* */
/********************************************************/
/* r0 nombre */
/* r1 exposant */
/* r2 modulo */
/* r0 return result */
moduloPuR32:
push {r1-r6,lr} @ save registers
cmp r0,#0 @ control <> zero
beq 100f
cmp r2,#0 @ control <> zero
beq 100f
1:
mov r4,r2 @ save modulo
mov r5,r1 @ save exposant
mov r6,r0 @ save base
mov r3,#1 @ start result
mov r1,#0 @ division r0,r1 by r2
bl division32R2023
mov r6,r2 @ base <- remainder
2:
tst r5,#1 @ exposant even or odd
beq 3f
umull r0,r1,r6,r3 @ multiplication base
mov r2,r4 @ and compute modulo N
bl division32R2023
mov r3,r2 @ result <- remainder
3:
umull r0,r1,r6,r6 @ compute base square
mov r2,r4 @ and compute modulo N
bl division32R2023
mov r6,r2 @ base <- remainder
lsr r5,#1 @ left shift 1 bit
cmp r5,#0 @ end ?
bne 2b
mov r0,r3
100:
pop {r1-r6,pc}
/***************************************************/
/* division number 64 bits in 2 registers by number 32 bits */
/* unsigned */
/***************************************************/
/* r0 contains lower part dividende */
/* r1 contains upper part dividende */
/* r2 contains divisor */
/* r0 return lower part quotient */
/* r1 return upper part quotient */
/* r2 return remainder */
division32R2023:
push {r3-r6,lr} @ save registers
mov r4,r2 @ save divisor
mov r5,#0 @ init upper part divisor
mov r2,r0 @ save dividende
mov r3,r1
mov r0,#0 @ init result
mov r1,#0
mov r6,#0 @ init shift counter
1: @ loop shift divisor
cmp r5,#0 @ upper divisor <0
blt 2f
cmp r5,r3
cmpeq r4,r2
bhs 2f @ new divisor > dividende
lsl r5,#1 @ shift left one bit upper divisor
lsls r4,#1 @ shift left one bit lower divisor
orrcs r5,r5,#1 @ move bit 31 lower on upper
add r6,r6,#1 @ increment shift counter
b 1b
2: @ loop 2
lsl r1,#1 @ shift left one bit upper quotient
lsls r0,#1 @ shift left one bit lower quotient
orrcs r1,#1 @ move bit 31 lower on upper
cmp r5,r3 @ compare divisor and dividende
cmpeq r4,r2
bhi 3f
subs r2,r2,r4 @ < sub divisor from dividende lower
sbc r3,r3,r5 @ and upper
orr r0,r0,#1 @ move 1 on quotient
3:
lsr r4,r4,#1 @ shift right one bit upper divisor
lsrs r5,#1 @ and lower
orrcs r4,#0x80000000 @ move bit 0 upper to 31 bit lower
subs r6,#1 @ decrement shift counter
bge 2b @ if > 0 loop 2
100:
pop {r3-r6,pc}
/***************************************************/
/* Generation random number */
/***************************************************/
/* r0 contains limit */
genereraleas:
push {r1-r4,lr} @ save registers
ldr r4,iAdriGraine
ldr r2,[r4]
ldr r3,iNbDep1
mul r2,r3,r2
ldr r3,iNbDep1
add r2,r2,r3
str r2,[r4] @ save seed for next call
cmp r0,#0
beq 100f
mov r1,r0 @ divisor
mov r0,r2 @ dividende
bl division
mov r0,r3 @ résult = remainder
100: @ end function
pop {r1-r4,pc} @ restaur registers
iAdriGraine: .int iGraine
iNbDep1: .int 0x343FD
iNbDep2: .int 0x269EC3
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
/* for this file see task include a file in arm assembly */
.include "../affichage.inc"- Output:
Program 32 bits start Prime N0 10001 : 104743 Program normal end.
Arturo
primes: select 2..110000 => prime?
print primes\[10000]
- Output:
104743
AWK
Converted from FreeBASIC
# syntax: GAWK -f 10001TH_PRIME.AWK
BEGIN {
printf("%s\n",main(10001))
exit(0)
}
function main(n, p,pn) {
if (n == 1) { return(2) }
p = 3
pn = 1
while (pn < n) {
if (is_prime(p)) {
pn++
}
p += 2
}
return(p-2)
}
function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
}
Idiomatic
# awk -f 10001prime.awk
# n: odd number and n>8
function IsOddPrime(n, i,limit) {
limit = int(sqrt(n))
for (i=3;i <= limit;i+=2)
if (n%i==0) return 0
return 1
}
# pos: positive
function PrimePosition(pos, prime){
pos -= ( (pos==1) ? prime=2 : prime=3 ) - 1
while (pos)
if (IsOddPrime(prime+=2)) pos--
return prime
}
BEGIN { print PrimePosition(10001) }
- Output:
104743
BASIC
BASIC256
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
function prime(n)
if n=1 then return 2
p = 3
pn = 1
while pn < n
if isPrime(p) then pn += 1
p += 2
end while
return p-2
end function
print prime(10001)
endChipmunk Basic
The GW-BASIC solution works without any changes.
FreeBASIC
#include "isprime.bas"
function prime( n as uinteger ) as ulongint
if n=1 then return 2
dim as integer p=3, pn=1
while pn<n
if isprime(p) then pn + = 1
p += 2
wend
return p-2
end function
print prime(10001)
- Output:
104743
Gambas
'Use "isprime.bas"
Public Sub Main()
Print prime(10001)
End
Function prime(n As Integer) As Long
If n = 1 Then Return 2
Dim p As Integer = 3, pn As Integer = 1
While pn < n
If isPrime(p) Then pn += 1
p += 2
Wend
Return p - 2
End Function
- Output:
104743
GW-BASIC
10 PN = 1
20 P = 3
30 WHILE PN < 10001
40 GOSUB 100
50 IF Q = 1 THEN PN = PN + 1
60 P = P + 2
70 WEND
80 PRINT P - 2
90 END
100 REM Tests if a number is prime
110 Q = 0
120 IF P = 2 THEN Q = 1: RETURN
130 IF P = 3 THEN Q = 1: RETURN
140 I = 1
150 I = I + 2
160 IF INT(P / I) * I = P THEN RETURN
170 IF I * I <= P THEN GOTO 150
180 Q = 1
190 RETURN
- Output:
104743
PureBasic
Procedure isPrime(v.i)
If v <= 1 : ProcedureReturn #False
ElseIf v < 4 : ProcedureReturn #True
ElseIf v % 2 = 0 : ProcedureReturn #False
ElseIf v < 9 : ProcedureReturn #True
ElseIf v % 3 = 0 : ProcedureReturn #False
Else
Protected r = Round(Sqr(v), #PB_Round_Down)
Protected f = 5
While f <= r
If v % f = 0 Or v % (f + 2) = 0
ProcedureReturn #False
EndIf
f + 6
Wend
EndIf
ProcedureReturn #True
EndProcedure
Procedure prime(n.i)
If n = 1
ProcedureReturn 2
EndIf
p.i = 3
pn.i = 1
While pn < n
If isprime(p)
pn + 1
EndIf
p + 2
Wend
ProcedureReturn p-2
EndProcedure
OpenConsole()
n = prime(10001)
PrintN(Str(n))
CloseConsole()
QB64
Trial Division Method
max=10001: n=1: p=0: t=Timer ' PRIMES.bas russian DANILIN
While n <= max ' 10001 104743 0.35 seconds
f=0: j=2
While f < 1
If j >= p ^ 0.5 Then f=2
If p Mod j = 0 Then f=1
j=j+1
Wend
If f <> 1 Then n=n+1: ' Print n, p
p=p+1
Wend
Print n-1, p-1, Timer-t
- Output:
10001 104743 0.35 seconds
More Efficient TD Method
'JRace's results:
'Original version: 10001 104743 .21875
'This version: 10001 104743 .109375
max = 10001: n=1: p=0: t = Timer ' PRIMES.bas
While n <= max ' 10001 104743 0.35 seconds
f = 0: j = 2
pp = p^0.5 'NEW VAR: move exponentiation here, to outer loop
While f < 1
' If j >= p ^ 0.5 Then f=2 'original line
' NOTE: p does not change in this loop,
' therefore p^0.5 doesn't change;
' moving p^0.5 to the outer loop will eliminate a lot of FP math)
If j >= pp Then f=2 'new version with exponentiation relocated
If p Mod j = 0 Then f=1
j=j+1
Wend
If f <> 1 Then n=n+1: ' Print n, p
p=p+1
Wend
Print n-1, p-1, Timer - t
- Output:
10001 104743 0.11 seconds
True BASIC
Trial Division Method
LET max = 10001
LET n = 1
LET p = 0
DO WHILE n <= max
LET f = 0
LET j = 2
DO WHILE f < 1
IF j >= p^0.5 THEN LET f = 2
IF REMAINDER(p, j) = 0 THEN LET f = 1
LET j = j+1
LOOP
IF f <> 1 THEN LET n = n+1
LET p = p+1
LOOP
PRINT p-1
END
- Output:
104743
Yabasic
sub isPrime(v)
if v < 2 then return False : fi
if mod(v, 2) = 0 then return v = 2 : fi
if mod(v, 3) = 0 then return v = 3 : fi
d = 5
while d * d <= v
if mod(v, d) = 0 then return False else d = d + 2 : fi
wend
return True
end sub
sub prime(n)
if n = 1 then return 2 : fi
p = 3
pn = 1
while pn<n
if isPrime(p) then pn = pn + 1 : fi
p = p + 2
wend
return p-2
end sub
print prime(10001)
endbc
a[0] = 2
a[o = 1] = 3
for (n = 5; o < 10000; n += 2) {
for (i = 1; n % (p = a[i]) != 0; ++i) {
if (p * p > n) {
a[++o] = n
break
}
}
}
a[o]
- Output:
104743
C
#include<stdio.h>
#include<stdlib.h>
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int prime( int n ) {
int p, pn=1;
if(n==1) return 2;
for(p=3;pn<n;p+=2) {
if(isprime(p)) pn++;
}
return p-2;
}
int main(void) {
printf( "%d\n", prime(10001) );
return 0;
}
- Output:
104743
C#
Sieve vs Trial Division
Comparing performance of the one-at-a-time trial division method vs the sieve of Eratosthenes method. About ten times faster for the sieve. It may appear that the sieve may be off by one, pr[10000] but since the array is zero based, it's the 10001st value.
using System; class Program {
static bool isprime(uint p ) { if ((p & 1) == 0) return p == 2;
if ((p % 3) == 0) return p == 3;
for (uint i = 5, d = 4; i * i <= p; i += (d = 6 - d))
if (p % i == 0) return false; return true; }
static uint prime(uint n) { uint p, d, pn;
for (p = 5, d = 4, pn = 2; pn < n; p += (d = 6 - d))
if (isprime(p)) pn++; return p - d; }
static void Main(string[] args) {
Console.WriteLine("One-at-a-time trial division vs sieve of Eratosthenes");
var sw = System.Diagnostics.Stopwatch.StartNew();
var t = prime(10001); sw.Stop(); double e1, e2;
Console.Write("{0:n0} {1} ms", prime(10001),
e1 = sw.Elapsed.TotalMilliseconds);
sw.Restart(); uint n = 105000, i, j; var pr = new uint[10100];
pr[0] = 2; pr[1] = 3; uint pc = 2, r, d, ii;
var pl = new bool[n + 1]; r = (uint)Math.Sqrt(n);
for (i = 9; i < n; i += 6) pl[i] = true;
for (i = 5, d = 4; i <= r; i += (d = 6 - d)) if (!pl[i]) {
pr[pc++] = i; for (j = i * i, ii = i << 1; j <= n; j += ii)
pl[j] = true; }
for ( ;i <= n; i += (d = 6 - d)) if (!pl[i]) pr[pc++] = i;
t = pr[10000]; sw.Stop();
Console.Write(" {0:n0} {1} μs {2:0.000} times faster", t,
(e2 = sw.Elapsed.TotalMilliseconds) * 1000.0, e1 / e2); } }
- Output @ Tio.run:
One-at-a-time trial division vs sieve of Eratosthenes 104,743 3.8943 ms 104,743 357.9 μs 10.881 times faster
Alternative Trial Division Method
using System; using System.Text; // PRIME_numb.cs russian DANILIN
namespace p10001 // 1 second 10001 104743
{ class Program // rextester.com/ZBEPGE34760
{ static void Main(string[] args)
{ int max=10001; int n=1; int p=1; int f; int j; long s;
while (n <= max)
{ f=0; j=2; s=Convert.ToInt32(Math.Pow(p,0.5));
while (f < 1)
{ if (j >= s)
{ f=2; }
if (p % j == 0) { f=1; }
j++;
}
if (f != 1) { n++; } // Console.WriteLine("{0} {1}", n, p);
p++;
}
Console.Write("{0} {1}", n-1, p-1);
Console.ReadKey();
}}}
- Output:
104743
C++
#include <iostream>
#include <locale>
#include <primesieve.hpp>
int main() {
std::cout.imbue(std::locale(""));
std::cout << "The 10,001st prime is " << primesieve::nth_prime(10001) << ".\n";
}
- Output:
The 10,001st prime is 104,743.
COBOL
Limit based on the fact that the nth prime is guaranteed to be less than n * (ln n + ln(ln n)).
IDENTIFICATION DIVISION.
PROGRAM-ID. 10001th_prime.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 n PIC 9(3) COMP.
01 cnt PIC 9(5) COMP VALUE 1.
01 sieve.
05 isp PIC 9 VALUE 1 OCCURS 115000 TIMES
INDEXED BY i.
01 out PIC Z(10).
PROCEDURE DIVISION.
PERFORM VARYING n FROM 2 BY 1 UNTIL n * n > 115000
SET i TO n
IF isp(i) = 1
MULTIPLY n BY n GIVING i
PERFORM VARYING i FROM i BY n UNTIL i > 115000
SET isp(i) TO 0
END-PERFORM
END-PERFORM
SET i to 1
PERFORM UNTIL cnt = 10001
SET i UP BY 2
ADD isp(i) TO cnt
END-PERFORM
MOVE i TO out
DISPLAY FUNCTION TRIM (out)
STOP RUN.
- Output:
104743
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;
}
int prime(int n) {
int p, pn = 1;
if (n == 1) return 2;
for (p = 3; pn < n; p += 2) {
if (isPrime(p)) pn++;
}
return p - 2;
}
void main() {
print(prime(10001));
}
- Output:
104743
Delphi
function IsPrime(N: integer): boolean;
{Fast, optimised prime test}
var I,Stop: integer;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function Find10001thPrime: integer;
{Return the 10,001th prime number}
var Count: integer;
begin
Count:=1;
Result:= 3;
while true do
begin
if IsPrime(Result) then Count:= Count+1;
if Count=10001 then exit;
Inc(Result,2);
end;
end;
- Output:
10,001th Prime= 104,743
D
import std.stdio;
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int prime( int n ) {
if(n==1) return 2;
int p, pn=1;
for(p=3;pn<n;p+=2) {
if(isprime(p)) pn++;
}
return p-2;
}
void main()
{
writeln(prime(10_001));
}
- Output:
104743
DuckDB
# Is nnumber prime?
create or replace function primep(nnumber) as (
select
case
when nnumber < 2 then false
when nnumber = 2 then true
else NOT exists
( select * from
( select (nnumber % anumber) as modNumber
from (select unnest(range(2, 1 + sqrt(nnumber)::BIGINT)) as anumber)
)
where modNumber = 0
)
end
);
create or replace function nth_prime(n) as (
if (n <= 0, 0,
if (n = 1, 2,
(with recursive cte as (
select 2 as prime, 3 as candidate, true as pprime, 1 as nth
union all
select if(pprime, candidate, prime) as prime,
candidate+2 as candidate,
primep(candidate+2) as pprime,
if(pprime,1,0)+nth as nth
from cte
where nth < n
)
select prime from cte where nth = n
)))
);
select nth_prime(10001)
- Output:
┌──────────────────┐ │ nth_prime(10001) │ │ int32 │ ├──────────────────┤ │ 104743 │ └──────────────────┘
Erlang
-module(task_10001th_prime).
-export([main/0]).
% 2 and 3 are both primes, so we start searching at 5
main() -> search(5, 2, 2).
search(N, Inc, Count) when Count < 10_001 ->
case is_prime(N) of
true -> search(N + Inc, 6 - Inc, Count + 1);
false -> search(N + Inc, 6 - Inc, Count)
end;
search(N, Inc, _) -> N - 6 + Inc.
is_prime(P) -> is_prime(P, 5, 2).
is_prime(N, P, _) when P * P > N -> true;
is_prime(N, P, _) when N rem P =:= 0 -> false;
is_prime(N, P, Inc) -> is_prime(N, P + Inc, 6 - Inc).
- Output:
timer:tc(task_10001th_prime, main, []).
{68615,104743}
EasyLang
fastfunc isprim num .
i = 3
while i <= sqrt num
if num mod i = 0
return 0
.
i += 2
.
return 1
.
nprim = 1
i = 3
repeat
if isprim i = 1
nprim += 1
.
until nprim = 10001
i += 2
.
print i- Output:
104743
F#
This task uses Extensible Prime Generator (F#)
// 10001st prime. Nigel Galloway: November 22nd., 2021
printfn $"%d{Seq.item 10000 (primes32())}"
- Output:
104743
Factor
USING: math math.primes prettyprint ;
2 10,000 [ next-prime ] times .
- Output:
104743
Fermat
Prime(10001);
- Output:
104743
Frink
nth1[primes[], 10001]- Output:
104743
FutureBasic
local fn IsPrime( n as NSUInteger ) as BOOL
BOOL isPrime = YES
NSUInteger i
if n < 2 then exit fn = NO
if n = 2 then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime
local fn Prime( n as NSUInteger ) as long
long p = 3, pn = 1
if n = 1 then exit fn = 2
while ( pn < n )
if fn IsPrime( p ) then pn++
p += 2
wend
p -= 2
end fn = p
print fn Prime(10001)
HandleEvents- Output:
104743
Go
package main
import "fmt"
func isPrime(n int) bool {
if n == 1 {
return false
}
i := 2
for i*i <= n {
if n%i == 0 {
return false
}
i++
}
return true
}
func main() {
var final, pNum int
for i := 1; pNum < 10001; i++ {
if isPrime(i) {
pNum++
}
final = i
}
fmt.Println(final)
}
- Output:
104743
Haskell
Relying upon the nontrivial fact that for every natural n >= 3 there exists a prime p with sqrt(n) < p < n to avoid looping infinitely:
primes :: [Int]
primes = (2 :) $ filter ( \n -> and $ map ((/= 0) . (rem n)) $ takeWhile ((<= n) . (^ 2)) $ primes ) $ [3,5..]
main = print $ primes !! 10000
- Output:
104743
J
p:10000 NB. the index starts at 0; p:0 = 2
- Output:
104743
Java
Uses the PrimeGenerator class from Extensible prime generator#Java.
public class NthPrime {
public static void main(String[] args) {
System.out.printf("The 10,001st prime is %,d.\n", nthPrime(10001));
}
private static int nthPrime(int n) {
assert n > 0;
PrimeGenerator primeGen = new PrimeGenerator(10000, 100000);
int prime = primeGen.nextPrime();
while (--n > 0)
prime = primeGen.nextPrime();
return prime;
}
}
- Output:
The 10,001st prime is 104,743.
JavaScript
Prime 10001 from Russia jdoodle.com/h/2V1
var max = 10001, n=1, p=1; var f,j,s
while (n <= max)
{ f=0; j=2; s = parseInt(Math.pow(p, 0.5))
while (f < 1)
{ if (j >= s) f=2
if ( p % j == 0 ) f=1
j++
}
if (f != 1) n++ // { document.write(n +" "+ p +"<br>") }
p++
}
document.write("<br>"+ (n-1) +" "+ (p-1) +"<br>" )
- Output:
10001 104743
jq
Works with gojq, the Go implementation of jq
A solution without any pre-determined numbers or guesses.
See Erdős-primes#jq for a suitable definition of `is_prime` as used here.
# Output: a stream of the primes
def primes: 2, (range(3; infinite; 2) | select(is_prime));
# The task
# jq uses an index-origin of 1 and so:
nth(10000; primes)- Output:
104743
Julia
julia> using Primes
julia> prime(10001)
104743
Mathematica / Wolfram Language
Prime[10001]
- Output:
104743
Maxima
primes_first_n(n) := (
if n<=1 then
[]
else (
L : [2],
for i:2 thru n do (
L : append(L, [next_prime(last(L))])
),
L
)
)$
last(primes_first_n(10001));
- Output:
104743
MiniScript
isPrime = function(n)
s = floor(n ^ 0.5)
for i in range(2, s)
if n % i == 0 then return false
end for
return true
end function
tt = time
c = 2
p = 2
lastPrime = 2
while c < 10001
p += 1
if isPrime(p) then
c += 1
end if
end while
print p
- Output:
104743
Nim
func isPrime(n: Positive): bool =
## Return true if "n" is prime.
## Assume n >= 5 and n not multiple of 2 and 3.
var d = 5
var step = 2
while d * d <= n:
if n mod d == 0:
return false
inc d, step
step = 6 - step
result = true
iterator primes(): tuple[rank, value: int] =
## Yield the primes preceded by their rank in the sequence.
yield (1, 2)
yield (2, 3)
var idx = 2
var n = 5
var step = 2
while true:
if n.isPrime:
inc idx
yield (idx, n)
inc n, step
step = 6 - step
for (i, n) in primes():
if i == 10001:
echo "10001st prime: ", n
break
- Output:
10001st prime: 104743
OCaml
Using the function seq_primes from Extensible prime generator#OCaml:
let () =
seq_primes |> Seq.drop 10000 |> Seq.take 1 |> Seq.iter (Printf.printf "%u\n")
- Output:
104743
PARI/GP
prime(10001)- Output:
%1 = 104743
Pascal
Free Pascal
Program nth_prime;
Function nthprime(x : uint32): uint32;
Var primes : array Of uint32;
i,pr,count : uint32;
found : boolean;
Begin
setlength(primes, x);
primes[1] := 2;
count := 1;
i := 3;
Repeat
found := FALSE;
pr := 0;
Repeat
inc(pr);
found := i Mod primes[pr] = 0;
Until (primes[pr]*primes[pr] > i) Or found;
If Not found Then
Begin
inc(count);
primes[count] := i;
End;
inc(i,2);
Until count = x;
nthprime := primes[x];
End;
Begin
writeln(nthprime(10001));
End.
- Output:
104743
Perl
use strict;
use warnings;
use feature 'say';
# the lengthy wait increases the delight in finally seeing the answer
my($n,$c) = (1,0);
while () {
$c++ if (1 x ++$n) !~ /^(11+)\1+$/;
$c == 10_001 and say $n and last;
}
# or if for some reason you want the answer quickly
use ntheory 'nth_prime';
say nth_prime(10_001);
- Output:
104743 104743
Phix
with js ?get_prime(10001)
- Output:
104743
Picat
go ?=>
println(nth_prime(10001)),
% faster but probably considered cheating
nth(10001,primes(200000),P),
println(P).
nth_prime(Choosen) = P =>
nth_prime(1,0,Choosen, P).
nth_prime(Num, Choosen, Choosen, Num) :-
prime(Num).
nth_prime(Num, Ix, Choosen, P) :-
Ix < Choosen,
next_prime(Num, P2),
nth_prime(P2, Ix+1, Choosen, P).
next_prime(Num, P) :-
next_prime2(Num+1, P).
next_prime2(Num, Num) :-
prime(Num).
next_prime2(Num, P) :-
next_prime2(Num+1,P).- Output:
104743 104743
Prolog
for swi-prolog
isPrime(2). % prime generator
isPrime(N):-
between(3, inf, N),
N /\ 1 > 0, % odd
M is floor(sqrt(N)) - 1, % reverse 2*I+1
Max is M div 2,
forall(between(1, Max, I), N mod (2*I+1) > 0).
do:- Index is 10001,
findnsols(Index, N, isPrime(N), PrimeList),!,
last(PrimeList, PrimeAtIndex),
format('prime(~d) is ~d', [Index, PrimeAtIndex]), nl.
- Output:
?- do. prime(10001) is 104743 true.
Python
Trial Division Method
#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
def prime(n: int) -> int:
if n == 1:
return 2
p = 3
pn = 1
while pn < n:
if isPrime(p):
pn += 1
p += 2
return p-2
if __name__ == '__main__':
print(prime(10001))
- Output:
104743
Alternative Trial Division Method
import time; max=10001; n=1; p=1; # PRIME_numb.py russian DANILIN
while n<=max: # 78081 994271 45 seconds
f=0; j=2; s = int(p**0.5) # rextester.com/AAOHQ6342
while f < 1:
if j >= s:
f=2
if p % j == 0:
f=1
j+=1
if f != 1:
n+=1;
#print(n,p);
p+=1
print(n-1,p-1)
print(time.perf_counter())
- Output:
10001 104743 7 seconds
Quackery
The 10001st prime number is the 10000th odd prime number.
prime is defined at Miller–Rabin primality test#Quackery.
1 10000 times [ 2 + dup prime until ] echo- Output:
104743
R
library(primes)
nth_prime(10001)
- Output:
104743
Racket
#lang racket
(require math/number-theory)
; Index starts at 0, (nth-prime 0) is 2
(nth-prime 10000)
- Output:
104743
Raku
say (^∞).grep( &is-prime )[10000]
- Output:
104743
REXX
The task has no stretch goal, nevertheless I will try one: showing primes higher in de sequence.
Trial division
/* REXX */
Parse Version v
Say v
Call Time 'R'
z=1
p.0=3
p.1=2
p.2=3
p.3=5
Do n=5 By 2 Until z=10001
If right(n,1)=5 Then Iterate
Do i=2 To p.0 Until b**2>n
b=p.i
If n//b=0 Then Leave
End
If b**2>n Then Do
z=p.0+1
p.z=n
p.0=z
End
End
Say z n time('E')
- Output:
H:\>rexx prime10001 REXX-ooRexx_5.0.0(MT)_64-bit 6.05 8 Sep 2020 10001 104743 0.219000 H:\>regina prime10001 REXX-Regina_3.9.4(MT) 5.00 25 Oct 2021 10001 104743 .615000 Finding the 100001th prime number: REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022 100001 1299721 11.989000 REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024 100001 1299721 19.117000
Sieve
Libraries: How to use
Libraries: Source code
As some other REXX entries suggest, using a sieve is fast, but requires memory to store the primes. Consider following program, based on the property 'nth prime < n*(ln(n)+ln(ln(n)))'.
include Settings
say version; say '10001th prime'; say
call Primes(-10001)
say prim.prime.10001
say Format(Time('e'),,3) 'seconds'
exit
include Functions
include Numbers
include Sequences
include Constants
include Abend
- Output:
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024 10001th prime 104743 0.039 seconds
Ring
load "stdlib.ring"
see "working..." + nl
num = 0 pr = 0 limit = 10001
while true
num++
if isprime(num) pr++ ok
if pr = limit exit ok
end
see "" + num + nl + "done..." + nl- Output:
working... The 10001th prime is: 104743 done...
RPL
« 2
1 10000 START NEXTPRIME NEXT
» 'TASK' STO
- Output:
1: 104743
Ruby
require "prime"
puts Prime.lazy.drop(10_000).next
- Output:
104743
Rust
// [dependencies]
// primal = "0.3"
fn main() {
let p = primal::StreamingSieve::nth_prime(10001);
println!("The 10001st prime is {}.", p);
}
- Output:
The 10001st prime is 104743.
Scala
Scala3 ready
object Prime10001 extends App {
val oddPrimes: LazyList[Int] = 3 #:: LazyList.from(5, 2)
.filter(p => oddPrimes.takeWhile(_ <= math.sqrt(p)).forall(p % _ > 0))
val primes = 2 #:: oddPrimes
val index = 10_001
println(s"prime($index): " + primes.drop(index - 1).take(1).head)
}
- Output:
prime(10001): 104743
Sidef
say 10001.prime- Output:
104743
Wren
import "./math" for Int
import "./fmt" for Fmt
var n = 10001
var limit = (n.log * n * 1.2).floor // should be enough
var primes = Int.primeSieve(limit)
Fmt.print("The $,r prime is $,d.", n, primes[n-1])
- Output:
The 10,001st prime is 104,743.
x86 Assembly
Using the Sieve of Eratosthenes and n * (ln n + ln(ln n)) as the upper limit for finding the nth prime.
section .data
primes times 14375 db 255 ;N * (ln N + ln(ln N)) bits, rounded up
section .text
global main
main:
mov ebx, 1 ;array index for outer loop
xor ecx, ecx ;counter
sieve_outer:
inc ebx ;increase index
mov eax, ebx ;copy to eax for squaring
mul ebx ;square
cmp eax, 115000 ;check if square is > limit
jg find10001st ;if it is, sieve is done
bt [primes], ebx ;check if ebx is no prime
jnc sieve_outer ;if no prime, try next number
inc ecx ;else increase counter
sieve_inner:
btr [primes], eax ;set multiple to not prime
add eax, ebx ;next multiple
cmp eax, 115000 ;check if multiple is < limit
jl sieve_inner ;if it is, continue with inner loop
jmp sieve_outer ;if not, continue with outer loop
find10001st:
inc ebx ;increase array index
bt [primes], ebx ;is it prime?
adc ecx, 0 ;if yes, increase ecx
cmp ecx, 10001 ;check if counter arrived at 10001
jl find10001st ;if not, continue
;done, result in ebx
- Output:
104743
XPL0
func IsPrime(N); \Return 'true' if odd N > 2 is prime
int N, I;
[for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];
int C, N;
[C:= 1; \count 2 as first prime
N:= 3;
loop [if IsPrime(N) then
[C:= C+1;
if C = 10001 then quit;
];
N:= N+2;
];
IntOut(0, N);
]- Output:
104743
Zig
const std = @import("std");
const stdout = @import("std").io.getStdOut().writer();
const limit = 10001;
fn isPrime(x: usize) bool {
if (x % 2 == 0) return false;
var i: usize = 3;
while (i * i <= x) : (i += 2) {
if (x % i == 0) return false;
}
return true;
}
pub fn main() !void {
var cnt: usize = 0;
var last: usize = 0;
var n: usize = 1;
while (cnt < limit) : (n += 1) {
if (isPrime(n)) {
cnt += 1;
last = n;
}
}
try stdout.print("{d}st prime number is: {d}\n", .{ limit, last });
}
- Output:
10001st prime number is: 104743
Categories:
- Draft Programming Tasks
- 11l
- AArch64 Assembly
- Ada
- ALGOL 68
- ALGOL 68-primes
- ARM Assembly
- Arturo
- AWK
- BASIC
- BASIC256
- Chipmunk Basic
- FreeBASIC
- Gambas
- GW-BASIC
- PureBasic
- QB64
- True BASIC
- Yabasic
- Bc
- C
- C sharp
- C++
- Primesieve
- COBOL
- Dart
- Delphi
- None
- D
- DuckDB
- Erlang
- EasyLang
- F Sharp
- Factor
- Fermat
- Frink
- FutureBasic
- Go
- Haskell
- J
- Java
- JavaScript
- Jq
- Julia
- Mathematica
- Wolfram Language
- Maxima
- MiniScript
- Nim
- OCaml
- PARI/GP
- Pascal
- Free Pascal
- Perl
- Ntheory
- Phix
- Picat
- Prolog
- Python
- Quackery
- R
- Racket
- Raku
- REXX
- Ring
- RPL
- Ruby
- Rust
- Scala
- Sidef
- Wren
- Wren-math
- Wren-fmt
- X86 Assembly
- XPL0
- Zig