Find prime numbers of the form n*n*n+2
- Task
- Find prime numbers of the form n3+2, where 0 < n < 200
11l
F isPrime(n)
L(i) 2 .. Int(n ^ 0.5)
I n % i == 0
R 0B
R 1B
L(n) 1..199
I isPrime(n ^ 3 + 2)
print(n"\t"(n ^ 3 + 2))
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Ada
with Ada.Text_Io;
procedure Find_Primes is
type Number is new Long_Integer range 0 .. Long_Integer'Last;
package Number_Io is new Ada.Text_Io.Integer_Io (Number);
function Is_Prime (A : Number) return Boolean is
D : Number;
begin
if A < 2 then return False; end if;
if A in 2 .. 3 then return True; end if;
if A mod 2 = 0 then return False; end if;
if A mod 3 = 0 then return False; end if;
D := 5;
while D * D <= A loop
if A mod D = 0 then
return False;
end if;
D := D + 2;
if A mod D = 0 then
return False;
end if;
D := D + 4;
end loop;
return True;
end Is_Prime;
P : Number;
begin
Ada.Text_Io.Put_Line (" N N**3+2");
Ada.Text_Io.Put_Line ("------------");
for N in Number range 1 .. 199 loop
P := N**3 + 2;
if Is_Prime (P) then
Number_Io.Put (N, Width => 3); Ada.Text_Io.Put (" ");
Number_Io.Put (P, Width => 7);
Ada.Text_Io.New_Line;
end if;
end loop;
end Find_Primes;
- Output:
N N**3+2 ------------ 1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
ALGOL 68
BEGIN # Find n such that n^3 + 2 is a prime for n < 200 #
FOR n TO 199 DO
INT candidate = ( n * n * n ) + 2;
# there will only be 199 candidates, so a primality check by trial #
# division should be OK #
BOOL is prime := TRUE;
FOR f FROM 2 TO ENTIER sqrt( candidate )
WHILE is prime := candidate MOD f /= 0
DO SKIP OD;
IF is prime THEN
# n^3 + 2 is prime #
print( ( whole( n, -4 ), ": ", whole( candidate, -8 ), newline ) )
FI
OD
END
- Output:
1: 3 3: 29 5: 127 29: 24391 45: 91127 63: 250049 65: 274627 69: 328511 71: 357913 83: 571789 105: 1157627 113: 1442899 123: 1860869 129: 2146691 143: 2924209 153: 3581579 171: 5000213 173: 5177719 189: 6751271
ALGOL W
begin % Find n such that n^3 + 2 is a prime for n < 200 %
for n := 1 until 199 do begin
integer candidate;
logical isPrime;
candidate := ( n * n * n ) + 2;
% there will only be 199 candidates, so a primality check by trial %
% division should be OK %
isPrime := true;
for f := 2 until entier( sqrt( candidate ) ) do begin
isPrime := candidate rem f not = 0;
if not isPrime then goto endPrimalityCheck
end for_f ;
endPrimalityCheck:
if isPrime then begin
% n^3 + 2 is prime %
write( i_w := 4, s_w := 0, n, ": ", i_w := 8, candidate )
end if_isPrime
end for_n
end.
- Output:
1: 3 3: 29 5: 127 29: 24391 45: 91127 63: 250049 65: 274627 69: 328511 71: 357913 83: 571789 105: 1157627 113: 1442899 123: 1860869 129: 2146691 143: 2924209 153: 3581579 171: 5000213 173: 5177719 189: 6751271
Arturo
primes: []
loop 1..199 'i [
num: 2 + i^3
if prime? num ->
'primes ++ @[to :string i, to :string num]
]
loop primes [i, num][
prints pad i 4
print pad num 9
]
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Asymptote
bool isPrime(int v) {
if (v < 2) return false;
if (v == 2) return true;
if (v % 2 == 0) return false;
for (int i = 3; i <= sqrt(v) + 1; i += 2) {
if (v % i == 0) return false;
}
return true;
}
for (int n = 1; n <= 200; ++n) {
if (isPrime(n^3 + 2)) write(n, n^3 + 2);
}
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
AWK
# syntax: GAWK -f FIND_PRIME_NUMBERS_OF_THE_FORM_NNN2.AWK
BEGIN {
start = 1
stop = 200
for (n=start; n<=stop; n++) {
p = n*n*n + 2
if (is_prime(p)) {
printf("%3d %'10d\n",n,p)
count++
}
}
printf("Prime numbers %d-%d of the form n*n*n+2: %d\n",start,stop,count)
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
- Output:
1 3 3 29 5 127 29 24,391 45 91,127 63 250,049 65 274,627 69 328,511 71 357,913 83 571,789 105 1,157,627 113 1,442,899 123 1,860,869 129 2,146,691 143 2,924,209 153 3,581,579 171 5,000,213 173 5,177,719 189 6,751,271 Prime numbers 1-200 of the form n*n*n+2: 19
BASIC
BASIC256
Use the code from Primality by trial division#BASIC256 as an include.
include "isprime.kbs"
for n = 1 to 200
if isPrime(n ^ 3 + 2) then print n, n ^ 3 + 2
next n
- Output:
Similar to FreeBASIC entry.
FreeBASIC
Use the code from Primality by trial division#FreeBASIC as an include.
#include"isprime.bas"
for n as uinteger = 1 to 200
if isprime(n^3+2) then
print n, n^3+2
end if
next n
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Gambas
Public Sub Main()
Dim t0 As Float = Timer
For n As Integer = 1 To 200
If isPrime(n ^ 3 + 2) Then Print n, n ^ 3 + 2
Next
Print "Took"; Timer - t0; " seconds on i5 @3.20 GHz"
End
Public Sub isPrime(ValorEval As Long) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Long = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
Wend
Return True
End Function
- Output:
Same as FreeBASIC entry.
Just BASIC
Use the code from Primality by trial division#Liberty_BASIC as an include.
for n = 1 to 200
if isPrime(n ^ 3 + 2) then print n, n ^ 3 + 2
next n
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
- Output:
Same as FreeBASIC entry.
PureBasic
Use the code from Primality by trial division#PureBasic as an include.
XIncludeFile "isprime.pb"
If OpenConsole():
For n.i = 1 To 200
If isPrime(Pow(n, 3) + 2):
PrintN(Str(n) + #TAB$ + Str(Pow(n, 3) + 2))
EndIf
Next n
PrintN(#CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
- Output:
Same as FreeBASIC entry.
QBasic
DECLARE FUNCTION isPrime% (ValorEval!)
FOR n = 1 TO 200
IF isPrime(n ^ 3 + 2) THEN PRINT n, n ^ 3 + 2
NEXT n
FUNCTION isPrime% (ValorEval!)
STATIC i AS INTEGER
IF ValorEval = 2 THEN
isPrime = 1
ELSEIF ValorEval <= 1 OR ValorEval MOD 2 = 0 THEN
isPrime = 0
ELSE
isPrime = 1
FOR i = 3 TO INT(SQR(ValorEval)) STEP 2
IF ValorEval MOD i = 0 THEN
isPrime = 0
EXIT FUNCTION
END IF
NEXT i
END IF
END FUNCTION
- Output:
Same as FreeBASIC entry.
QB64
The QBasic solution works without any changes.
Run BASIC
for n = 1 to 200
if isPrime(n ^ 3 + 2) then print n; chr$(9); n ^ 3 + 2
next n
function isPrime(n)
if n < 2 then isPrime = 0 : goto [exit]
if n = 2 then isPrime = 1 : goto [exit]
if n mod 2 = 0 then isPrime = 0 : goto [exit]
isPrime = 1
for i = 3 to int(n^.5) step 2
if n mod i = 0 then isPrime = 0 : goto [exit]
next i
[exit]
end function
- Output:
Same as FreeBASIC entry.
True BASIC
FUNCTION isprime(v)
LET false = 0
LET true = 1
IF v <= 1 THEN LET isprime = false
IF v < 4 THEN LET isprime = true
IF REMAINDER(v, 2) = 0 THEN LET isprime = false
IF v < 9 THEN LET isprime = true
IF REMAINDER(v, 3) = 0 THEN
LET isprime = false
ELSE
LET r = INT(SQR(v))
LET f = 5
DO WHILE f <= r
IF REMAINDER(v, f) = 0 OR REMAINDER(v, (f+2)) = 0 THEN LET isprime = false
LET f = f+6
LOOP
END IF
LET isprime = true
END FUNCTION
FOR n = 1 TO 200
IF isprime(n^3+2)<>0 THEN PRINT n, n^3+2
NEXT n
END
- Output:
Same as FreeBASIC entry.
Yabasic
Use the code from Primality by trial division#Yabasic as an include.
import isprime
for n = 1 to 200
if isPrime(n ^ 3 + 2) print n, "\t", n ^ 3 + 2
next n
- Output:
Same as FreeBASIC entry.
C
#include <stdio.h>
#include <stdbool.h>
#include <locale.h>
bool isPrime(int n) {
int d;
if (n < 2) return false;
if (!(n%2)) return n == 2;
if (!(n%3)) return n == 3;
d = 5;
while (d*d <= n) {
if (!(n%d)) return false;
d += 2;
if (!(n%d)) return false;
d += 4;
}
return true;
}
int main() {
int n, p;
const int limit = 200;
setlocale(LC_ALL, "");
for (n = 1; n < limit; ++n) {
p = n*n*n + 2;
if (isPrime(p)) {
printf("n = %3d => n³ + 2 = %'9d\n", n, p);
}
}
return 0;
}
- Output:
n = 1 => n³ + 2 = 3 n = 3 => n³ + 2 = 29 n = 5 => n³ + 2 = 127 n = 29 => n³ + 2 = 24,391 n = 45 => n³ + 2 = 91,127 n = 63 => n³ + 2 = 250,049 n = 65 => n³ + 2 = 274,627 n = 69 => n³ + 2 = 328,511 n = 71 => n³ + 2 = 357,913 n = 83 => n³ + 2 = 571,789 n = 105 => n³ + 2 = 1,157,627 n = 113 => n³ + 2 = 1,442,899 n = 123 => n³ + 2 = 1,860,869 n = 129 => n³ + 2 = 2,146,691 n = 143 => n³ + 2 = 2,924,209 n = 153 => n³ + 2 = 3,581,579 n = 171 => n³ + 2 = 5,000,213 n = 173 => n³ + 2 = 5,177,719 n = 189 => n³ + 2 = 6,751,271
C++
#include <iomanip>
#include <iostream>
bool is_prime(unsigned int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (unsigned int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
int main() {
for (unsigned int n = 1; n < 200; n += 2) {
auto p = n * n * n + 2;
if (is_prime(p))
std::cout << std::setw(3) << n << std::setw(9) << p << '\n';
}
}
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
CLU
is_prime = proc (n: int) returns (bool)
if n<2 then return(false) end
if n//2=0 then return(n=2) end
if n//3=0 then return(n=3) end
d: int := 5
while d*d <= n do
if n//d=0 then return(false) end
d := d+2
if n//d=0 then return(false) end
d := d+4
end
return(true)
end is_prime
n3plus2_primes = iter (max: int) yields (int,int)
for n: int in int$from_to(1, max) do
p: int := n**3 + 2
if is_prime(p) then yield(n,p) end
end
end n3plus2_primes
start_up = proc ()
po: stream := stream$primary_output()
for n, p: int in n3plus2_primes(200) do
stream$puts(po, "n = ")
stream$putright(po, int$unparse(n), 3)
stream$puts(po, " => n^3 + 2 = ")
stream$putright(po, int$unparse(p), 7)
stream$putl(po, "")
end
end start_up
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24391 n = 45 => n^3 + 2 = 91127 n = 63 => n^3 + 2 = 250049 n = 65 => n^3 + 2 = 274627 n = 69 => n^3 + 2 = 328511 n = 71 => n^3 + 2 = 357913 n = 83 => n^3 + 2 = 571789 n = 105 => n^3 + 2 = 1157627 n = 113 => n^3 + 2 = 1442899 n = 123 => n^3 + 2 = 1860869 n = 129 => n^3 + 2 = 2146691 n = 143 => n^3 + 2 = 2924209 n = 153 => n^3 + 2 = 3581579 n = 171 => n^3 + 2 = 5000213 n = 173 => n^3 + 2 = 5177719 n = 189 => n^3 + 2 = 6751271
COBOL
IDENTIFICATION DIVISION.
PROGRAM-ID. N3-PLUS-2-PRIMES.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES.
03 N PIC 9(3).
03 N3PLUS2 PIC 9(7).
03 DIVISOR PIC 9(4).
03 DIV-SQ PIC 9(8).
03 DIV-CHECK PIC 9(4)V9(4).
03 FILLER REDEFINES DIV-CHECK.
05 FILLER PIC 9(4).
05 FILLER PIC 9(4).
88 DIVISIBLE VALUE ZERO.
03 FILLER REDEFINES N3PLUS2.
05 FILLER PIC 9(6).
05 FILLER PIC 9.
88 EVEN VALUE 0, 2, 4, 6, 8.
03 PRIME-FLAG PIC X.
88 PRIME VALUE '*'.
01 FORMAT.
03 FILLER PIC X(4) VALUE "N = ".
03 N-OUT PIC ZZ9.
03 FILLER PIC X(17) VALUE " => N ** 3 + 2 = ".
03 N3PLUS2-OUT PIC Z(6)9.
PROCEDURE DIVISION.
BEGIN.
PERFORM TRY-N VARYING N FROM 1 BY 1
UNTIL N IS GREATER THAN 200.
STOP RUN.
TRY-N.
COMPUTE N3PLUS2 = N ** 3 + 2.
PERFORM CHECK-PRIME.
IF PRIME,
MOVE N TO N-OUT,
MOVE N3PLUS2 TO N3PLUS2-OUT,
DISPLAY FORMAT.
CHECK-PRIME SECTION.
BEGIN.
MOVE SPACE TO PRIME-FLAG.
IF N3PLUS2 IS LESS THAN 5, GO TO TRIVIAL.
IF EVEN, GO TO CHECK-PRIME-DONE.
DIVIDE N3PLUS2 BY 3 GIVING DIV-CHECK.
IF DIVISIBLE, GO TO CHECK-PRIME-DONE.
MOVE ZERO TO DIV-SQ.
MOVE 5 TO DIVISOR.
MOVE '*' TO PRIME-FLAG.
PERFORM CHECK-DIVISOR
UNTIL NOT PRIME OR DIV-SQ IS GREATER THAN N3PLUS2.
GO TO CHECK-PRIME-DONE.
CHECK-DIVISOR.
MULTIPLY DIVISOR BY DIVISOR GIVING DIV-SQ.
DIVIDE N3PLUS2 BY DIVISOR GIVING DIV-CHECK.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
ADD 2 TO DIVISOR.
DIVIDE N3PLUS2 BY DIVISOR GIVING DIV-CHECK.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
ADD 4 TO DIVISOR.
TRIVIAL.
IF N3PLUS2 IS EQUAL TO 2 OR EQUAL TO 3,
MOVE '*' TO PRIME-FLAG.
CHECK-PRIME-DONE.
EXIT.
- Output:
N = 1 => N ** 3 + 2 = 3 N = 3 => N ** 3 + 2 = 29 N = 5 => N ** 3 + 2 = 127 N = 29 => N ** 3 + 2 = 24391 N = 45 => N ** 3 + 2 = 91127 N = 63 => N ** 3 + 2 = 250049 N = 65 => N ** 3 + 2 = 274627 N = 69 => N ** 3 + 2 = 328511 N = 71 => N ** 3 + 2 = 357913 N = 83 => N ** 3 + 2 = 571789 N = 105 => N ** 3 + 2 = 1157627 N = 113 => N ** 3 + 2 = 1442899 N = 123 => N ** 3 + 2 = 1860869 N = 129 => N ** 3 + 2 = 2146691 N = 143 => N ** 3 + 2 = 2924209 N = 153 => N ** 3 + 2 = 3581579 N = 171 => N ** 3 + 2 = 5000213 N = 173 => N ** 3 + 2 = 5177719 N = 189 => N ** 3 + 2 = 6751271
Cowgol
include "cowgol.coh";
sub is_prime(n: uint32): (p: uint8) is
p := 0;
if n<=4 then
if n==2 or n==3 then
p := 1;
end if;
return;
end if;
if n&1 == 0 or n%3 == 0 then
return;
end if;
var d: uint32 := 5;
while d*d <= n loop
if n%d==0 then return; end if;
d := d+2;
if n%d==0 then return; end if;
d := d+4;
end loop;
p := 1;
end sub;
var n: uint32 := 1;
while n < 200 loop
var p: uint32 := n*n*n + 2;
if is_prime(p) != 0 then
print("n = ");
print_i32(n);
print("\t=> n^3 + 2 = ");
print_i32(p);
print_nl();
end if;
n := n+1;
end loop;
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24391 n = 45 => n^3 + 2 = 91127 n = 63 => n^3 + 2 = 250049 n = 65 => n^3 + 2 = 274627 n = 69 => n^3 + 2 = 328511 n = 71 => n^3 + 2 = 357913 n = 83 => n^3 + 2 = 571789 n = 105 => n^3 + 2 = 1157627 n = 113 => n^3 + 2 = 1442899 n = 123 => n^3 + 2 = 1860869 n = 129 => n^3 + 2 = 2146691 n = 143 => n^3 + 2 = 2924209 n = 153 => n^3 + 2 = 3581579 n = 171 => n^3 + 2 = 5000213 n = 173 => n^3 + 2 = 5177719 n = 189 => n^3 + 2 = 6751271
Delphi
program Find_prime_numbers_of_the_form_n_n_n_plus_2;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
PrimTrial;
function Commatize(n: NativeInt): string;
var
fmt: TFormatSettings;
begin
fmt := TFormatSettings.Create('en-Us');
Result := double(n).ToString(ffNumber, 64, 0, fmt);
end;
const
limit = 200;
begin
for var n := 1 to limit - 1 do
begin
var p := n * n * n + 2;
if isPrime(p) then
writeln('n = ', n: 3, ' => n^3 + 2 = ', Commatize(p): 9);
end;
readln;
end.
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24,391 n = 45 => n^3 + 2 = 91,127 n = 63 => n^3 + 2 = 250,049 n = 65 => n^3 + 2 = 274,627 n = 69 => n^3 + 2 = 328,511 n = 71 => n^3 + 2 = 357,913 n = 83 => n^3 + 2 = 571,789 n = 105 => n^3 + 2 = 1,157,627 n = 113 => n^3 + 2 = 1,442,899 n = 123 => n^3 + 2 = 1,860,869 n = 129 => n^3 + 2 = 2,146,691 n = 143 => n^3 + 2 = 2,924,209 n = 153 => n^3 + 2 = 3,581,579 n = 171 => n^3 + 2 = 5,000,213 n = 173 => n^3 + 2 = 5,177,719 n = 189 => n^3 + 2 = 6,751,271
Dart
import 'dart:math';
void main() {
for (var n = 1; n < 201; n++) {
if (isPrime(pow(n, 3) + 2)) {
print('$n \t ${pow(n, 3) + 2}');
}
}
}
bool isPrime(var 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;
}
- Output:
Similar to FreeBASIC entry.
Draco
proc nonrec is_prime(ulong n) bool:
ulong d;
bool prime;
if n<=4 then n=2 or n=3
elif n&1=0 or n%3=0 then false
else
d := 5;
prime := true;
while prime and d*d <= n do
if n%d=0 then prime := false fi;
d := d+2;
if n%d=0 then prime := false fi;
d := d+4
od;
prime
fi
corp
proc nonrec main() void:
word n;
ulong p;
for n from 1 upto 200 do
p := make(n,ulong);
p := p*p*p + 2;
if is_prime(p) then
writeln("n = ", n:3, " => n^3 + 2 = ", p:7)
fi
od
corp
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24391 n = 45 => n^3 + 2 = 91127 n = 63 => n^3 + 2 = 250049 n = 65 => n^3 + 2 = 274627 n = 69 => n^3 + 2 = 328511 n = 71 => n^3 + 2 = 357913 n = 83 => n^3 + 2 = 571789 n = 105 => n^3 + 2 = 1157627 n = 113 => n^3 + 2 = 1442899 n = 123 => n^3 + 2 = 1860869 n = 129 => n^3 + 2 = 2146691 n = 143 => n^3 + 2 = 2924209 n = 153 => n^3 + 2 = 3581579 n = 171 => n^3 + 2 = 5000213 n = 173 => n^3 + 2 = 5177719 n = 189 => n^3 + 2 = 6751271
EasyLang
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
for n = 1 to 199
p = pow n 3 + 2
if isprim p = 1
write p & " "
.
.
- Output:
3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271
F#
This task uses Extensible Prime Generator (F#).
[1..2..200]|>Seq.filter(fun n->isPrime(2+pown n 3))|>Seq.iter(fun n->printfn "n=%3d -> %d" n (2+pown n 3))
- Output:
n= 1 -> 3 n= 3 -> 29 n= 5 -> 127 n= 29 -> 24391 n= 45 -> 91127 n= 63 -> 250049 n= 65 -> 274627 n= 69 -> 328511 n= 71 -> 357913 n= 83 -> 571789 n=105 -> 1157627 n=113 -> 1442899 n=123 -> 1860869 n=129 -> 2146691 n=143 -> 2924209 n=153 -> 3581579 n=171 -> 5000213 n=173 -> 5177719 n=189 -> 6751271
Factor
Using the parity optimization from the Wren entry:
USING: formatting kernel math math.functions math.primes
math.ranges sequences tools.memory.private ;
1 199 2 <range> [
dup 3 ^ 2 + dup prime?
[ commas "n = %3d => n³ + 2 = %9s\n" printf ] [ 2drop ] if
] each
Or, using local variables:
USING: formatting kernel math math.primes math.ranges sequences
tools.memory.private ;
[let
199 :> limit
1 limit 2 <range> [| n |
n n n * * 2 + :> p
p prime?
[ n p commas "n = %3d => n³ + 2 = %9s\n" printf ] when
] each
]
- Output:
n = 1 => n³ + 2 = 3 n = 3 => n³ + 2 = 29 n = 5 => n³ + 2 = 127 n = 29 => n³ + 2 = 24,391 n = 45 => n³ + 2 = 91,127 n = 63 => n³ + 2 = 250,049 n = 65 => n³ + 2 = 274,627 n = 69 => n³ + 2 = 328,511 n = 71 => n³ + 2 = 357,913 n = 83 => n³ + 2 = 571,789 n = 105 => n³ + 2 = 1,157,627 n = 113 => n³ + 2 = 1,442,899 n = 123 => n³ + 2 = 1,860,869 n = 129 => n³ + 2 = 2,146,691 n = 143 => n³ + 2 = 2,924,209 n = 153 => n³ + 2 = 3,581,579 n = 171 => n³ + 2 = 5,000,213 n = 173 => n³ + 2 = 5,177,719 n = 189 => n³ + 2 = 6,751,271
Fermat
for n=1,199 do if Isprime(n^3+2)=1 then !!(n,n^3+2) fi od
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Forth
: prime? ( n -- flag )
dup 2 < if drop false exit then
dup 2 mod 0= if 2 = exit then
dup 3 mod 0= if 3 = exit then
5
begin
2dup dup * >=
while
2dup mod 0= if 2drop false exit then
2 +
2dup mod 0= if 2drop false exit then
4 +
repeat
2drop true ;
: main
200 1 do
i i i * * 2 + dup prime? if
i 3 .r 9 .r cr
else
drop
then
2 +loop ;
main
bye
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Frink
for n = 1 to 199
if isPrime[n^3 + 2]
println["$n\t" + n^3+2]
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
FutureBasic
include "NSLog.incl"
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 FindSpecialPrimes
for NSUInteger n = 1 to 200
if fn IsPrime( n^3+2 ) then NSLog( @"n = %3d => n^3 + 2 =%8s", n, fn StringUTF8String( str(n^3+2) ) )
next
end fn
fn FindSpecialPrimes
HandleEvents
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24391 n = 45 => n^3 + 2 = 91127 n = 63 => n^3 + 2 = 250049 n = 65 => n^3 + 2 = 274627 n = 69 => n^3 + 2 = 328511 n = 71 => n^3 + 2 = 357913 n = 83 => n^3 + 2 = 571789 n = 105 => n^3 + 2 = 1157627 n = 113 => n^3 + 2 = 1442899 n = 123 => n^3 + 2 = 1860869 n = 129 => n^3 + 2 = 2146691 n = 143 => n^3 + 2 = 2924209 n = 153 => n^3 + 2 = 3581579 n = 171 => n^3 + 2 = 5000213 n = 173 => n^3 + 2 = 5177719 n = 189 => n^3 + 2 = 6751271
Go
package main
import "fmt"
func isPrime(n int) bool {
switch {
case n < 2:
return false
case n%2 == 0:
return n == 2
case n%3 == 0:
return n == 3
default:
d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}
}
func commatize(n int) string {
s := fmt.Sprintf("%d", n)
if n < 0 {
s = s[1:]
}
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
if n >= 0 {
return s
}
return "-" + s
}
func main() {
const limit = 200
for n := 1; n < limit; n++ {
p := n*n*n + 2
if isPrime(p) {
fmt.Printf("n = %3d => n³ + 2 = %9s\n", n, commatize(p))
}
}
}
- Output:
n = 1 => n³ + 2 = 3 n = 3 => n³ + 2 = 29 n = 5 => n³ + 2 = 127 n = 29 => n³ + 2 = 24,391 n = 45 => n³ + 2 = 91,127 n = 63 => n³ + 2 = 250,049 n = 65 => n³ + 2 = 274,627 n = 69 => n³ + 2 = 328,511 n = 71 => n³ + 2 = 357,913 n = 83 => n³ + 2 = 571,789 n = 105 => n³ + 2 = 1,157,627 n = 113 => n³ + 2 = 1,442,899 n = 123 => n³ + 2 = 1,860,869 n = 129 => n³ + 2 = 2,146,691 n = 143 => n³ + 2 = 2,924,209 n = 153 => n³ + 2 = 3,581,579 n = 171 => n³ + 2 = 5,000,213 n = 173 => n³ + 2 = 5,177,719 n = 189 => n³ + 2 = 6,751,271
J
([,.2+]^3:)@([#~1:p:2+]^3:) }.i.200x
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Java
public final class FindPrimeNumbersOfTheFormNCubedPlusTwo {
public static void main(String[] args) {
System.out.println(" n n³ + 2");
System.out.println("------------");
for ( int n = 1; n < 200; n += 2 ) {
int p = n * n * n + 2;
if ( isPrime(p) ) {
System.out.println(String.format("%-5d%d", n, p));
}
}
}
private static boolean isPrime(int number) {
if ( number % 2 == 0 ) {
return number == 2;
}
int k = 3;
while ( k * k <= number ) {
if ( number % k == 0 ) {
return false;
}
k += 2;
}
return true;
}
}
- Output:
n n³ + 2 ------------ 1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
jq
Works with gojq, the Go implementation of jq
Using a definition of `is_prime` such as can be found at Safe_primes_and_unsafe_primes:
range(1;200) | pow(.; 3) + 2 | select(is_prime)
- Output:
3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271
Julia
# Formatting output as in Go example.
using Primes, Formatting
isncubedplus2prime(x) = begin fx = x * x * x + 2; (isprime(fx), fx) end
tostring(x, fx) = "n = " * lpad(x, 3) * " => n³ + 2 =" * lpad(format(fx, commas=true), 10)
function filterprintresults(x_to_bool_and_fx, start, stop, stringify=(x, fx)->"$x $fx", doprint=true)
ncount = 0
println("Filtering $x_to_bool_and_fx for integers between $start and $stop:\n")
for n in start+1:stop-1
isone, result = x_to_bool_and_fx(n)
if isone
doprint && println(stringify(n, result))
ncount += 1
end
end
println("\nThe total found was $ncount.")
end
filterprintresults(isncubedplus2prime, 0, 200, tostring)
- Output:
n = 1 => n³ + 2 = 3 n = 3 => n³ + 2 = 29 n = 5 => n³ + 2 = 127 n = 29 => n³ + 2 = 24,391 n = 45 => n³ + 2 = 91,127 n = 63 => n³ + 2 = 250,049 n = 65 => n³ + 2 = 274,627 n = 69 => n³ + 2 = 328,511 n = 71 => n³ + 2 = 357,913 n = 83 => n³ + 2 = 571,789 n = 105 => n³ + 2 = 1,157,627 n = 113 => n³ + 2 = 1,442,899 n = 123 => n³ + 2 = 1,860,869 n = 129 => n³ + 2 = 2,146,691 n = 143 => n³ + 2 = 2,924,209 n = 153 => n³ + 2 = 3,581,579 n = 171 => n³ + 2 = 5,000,213 n = 173 => n³ + 2 = 5,177,719 n = 189 => n³ + 2 = 6,751,271 The total found was 19.
One-liner version
using Primes; println(filter(isprime, map(x -> x^3 + 2, 1:199)))
- Output:
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]
MAD
NORMAL MODE IS INTEGER
INTERNAL FUNCTION(P)
ENTRY TO PRIME.
WHENEVER P.L.2, FUNCTION RETURN 0B
WHENEVER P.E.P/2*2, FUNCTION RETURN P.E.2
WHENEVER P.E.P/3*3, FUNCTION RETURN P.E.3
D = 5
CHKDIV WHENEVER D*D.LE.P
WHENEVER P.E.P/D*D, FUNCTION RETURN 0B
D = D+2
WHENEVER P.E.P/D*D, FUNCTION RETURN 0B
D = D+4
TRANSFER TO CHKDIV
END OF CONDITIONAL
FUNCTION RETURN 1B
END OF FUNCTION
VECTOR VALUES FMT = $4HN = ,I3,S4,12HN*N*N + 2 = ,I7*$
THROUGH LOOP, FOR N=1, 1, N.GE.200
M = N*N*N + 2
WHENEVER PRIME.(M)
PRINT FORMAT FMT,N,M
END OF CONDITIONAL
LOOP CONTINUE
END OF PROGRAM
- Output:
N = 1 N*N*N + 2 = 3 N = 3 N*N*N + 2 = 29 N = 5 N*N*N + 2 = 127 N = 29 N*N*N + 2 = 24391 N = 45 N*N*N + 2 = 91127 N = 63 N*N*N + 2 = 250049 N = 65 N*N*N + 2 = 274627 N = 69 N*N*N + 2 = 328511 N = 71 N*N*N + 2 = 357913 N = 83 N*N*N + 2 = 571789 N = 105 N*N*N + 2 = 1157627 N = 113 N*N*N + 2 = 1442899 N = 123 N*N*N + 2 = 1860869 N = 129 N*N*N + 2 = 2146691 N = 143 N*N*N + 2 = 2924209 N = 153 N*N*N + 2 = 3581579 N = 171 N*N*N + 2 = 5000213 N = 173 N*N*N + 2 = 5177719 N = 189 N*N*N + 2 = 6751271
Mathematica /Wolfram Language
Select[Range[199]^3 + 2, PrimeQ]
- Output:
{3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271}
Nim
import strutils
func isPrime(n: Positive): bool =
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
if n mod d == 0: return false
inc d, 4
result = true
for n in 1..<200:
let p = n * n * n + 2
if p.isPrime:
echo ($n).align(3), " → ", p
- Output:
1 → 3 3 → 29 5 → 127 29 → 24391 45 → 91127 63 → 250049 65 → 274627 69 → 328511 71 → 357913 83 → 571789 105 → 1157627 113 → 1442899 123 → 1860869 129 → 2146691 143 → 2924209 153 → 3581579 171 → 5000213 173 → 5177719 189 → 6751271
PARI/GP
for(N=1,200,if(isprime(N^3+2),print(N," ",N^3+2)))
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Pascal
Free Pascal
program Find_prime_numbers_of_the_form_n_n_n_plus_2;
{$IFDEF FPC}
{$MODE DELPHI} {$Optimization ON,ALL} {$COPERATORS ON}{$CODEALIGN proc=16}
{$ENDIF}
{$IFDEF WINDOWS}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
PrimTrial;
type
myString = String[31];
function Numb2USA(n:Uint64):myString;
const
//extend s by the count of comma to be inserted
deltaLength : array[0..24] of byte =
(0,0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7);
var
pI :pChar;
i,j : NativeInt;
Begin
str(n,result);
i := length(result);
//extend s by the count of comma to be inserted
// j := i+ (i-1) div 3;
j := i+deltaLength[i];
if i<> j then
Begin
setlength(result,j);
pI := @result[1];
dec(pI);
while i > 3 do
Begin
//copy 3 digits
pI[j] := pI[i];
pI[j-1] := pI[i-1];
pI[j-2] := pI[i-2];
// insert comma
pI[j-3] := ',';
dec(i,3);
dec(j,4);
end;
end;
end;
function n3_2(n:Uint32):Uint64;inline;
begin
n3_2 := UInt64(n)*n*n+2;
end;
const
limit =200;//trunc(exp(ln((HIGH(UInt32)-2))/3));
var
p : Uint64;
n : Uint32;
begin
n := 1;
repeat
p := n3_2(n);
if isPrime(p) then
writeln('n = ', Numb2USA(n):4, ' => n^3 + 2 = ', Numb2USA(p): 10);
inc(n,2);// n must be odd for n > 0
until n > Limit;
{$IFDEF WINDOWS}
readln;
{$IFEND}
end.
- Output:
n = 1 => n^3 + 2 = 3 n = 3 => n^3 + 2 = 29 n = 5 => n^3 + 2 = 127 n = 29 => n^3 + 2 = 24,391 n = 45 => n^3 + 2 = 91,127 n = 63 => n^3 + 2 = 250,049 n = 65 => n^3 + 2 = 274,627 n = 69 => n^3 + 2 = 328,511 n = 71 => n^3 + 2 = 357,913 n = 83 => n^3 + 2 = 571,789 n = 105 => n^3 + 2 = 1,157,627 n = 113 => n^3 + 2 = 1,442,899 n = 123 => n^3 + 2 = 1,860,869 n = 129 => n^3 + 2 = 2,146,691 n = 143 => n^3 + 2 = 2,924,209 n = 153 => n^3 + 2 = 3,581,579 n = 171 => n^3 + 2 = 5,000,213 n = 173 => n^3 + 2 = 5,177,719 n = 189 => n^3 + 2 = 6,751,271
Perl
use strict;
use warnings;
use feature 'say';
use Math::AnyNum ':all'; # in order to handle large values
# basic task results
say join ' ', grep { is_prime $_ } map { $_**3 + 2 } grep { 0 != $_%2 } 1..199;
# generalize a bit, how many primes over a range of exponents and offsets?
say ' ' . sprintf '%4d'x11 , 1..10;
for my $e (1..10) {
printf '%2d ', $e;
for my $o (1..10) {
printf '%4d', scalar grep { is_prime $_ } map { $_**$e + $o } 1..199;
}
print "\n";
}
- Output:
3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271 1 2 3 4 5 6 7 8 9 10 1 46 45 44 44 43 43 42 42 42 42 2 34 17 29 34 12 19 49 19 24 32 3 1 19 26 25 23 17 18 0 28 20 4 30 13 20 1 7 12 28 7 6 11 5 1 12 14 14 11 7 15 17 12 3 6 1 5 19 11 3 2 24 0 7 11 7 1 10 8 8 7 9 7 6 9 8 8 7 7 7 1 2 5 9 5 1 8 9 1 5 7 7 5 5 6 0 9 6 10 1 3 3 9 3 1 5 3 2 1
Phix
function pn3p2(integer n) integer n3p2 = power(n,3)+2 return iff(is_prime(n3p2)?{n,n3p2}:0) end function sequence res = filter(apply(tagset(199,1,2),pn3p2),"!=",0) printf(1,"Found %d primes of the form n^3+2:\n",length(res)) papply(true,printf,{1,{"n = %3d => n^3+2 = %,9d\n"},res})
- Output:
Found 19 primes of the form n^3+2: n = 1 => n^3+2 = 3 n = 3 => n^3+2 = 29 n = 5 => n^3+2 = 127 n = 29 => n^3+2 = 24,391 n = 45 => n^3+2 = 91,127 n = 63 => n^3+2 = 250,049 n = 65 => n^3+2 = 274,627 n = 69 => n^3+2 = 328,511 n = 71 => n^3+2 = 357,913 n = 83 => n^3+2 = 571,789 n = 105 => n^3+2 = 1,157,627 n = 113 => n^3+2 = 1,442,899 n = 123 => n^3+2 = 1,860,869 n = 129 => n^3+2 = 2,146,691 n = 143 => n^3+2 = 2,924,209 n = 153 => n^3+2 = 3,581,579 n = 171 => n^3+2 = 5,000,213 n = 173 => n^3+2 = 5,177,719 n = 189 => n^3+2 = 6,751,271
Plain English
To run:
Start up.
Put 1 into a counter.
Loop.
Put the counter into a number.
Raise the number to 3.
Add 2 to the number.
If the number is prime, write the counter then " " then the number on the console.
Add 2 to the counter.
If the counter is greater than 200, break.
Repeat.
Write "Done." on the console.
Wait for the escape key.
Shut down.
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271 Done.
Python
#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
if __name__ == '__main__':
for n in range(1, 200):
if isPrime(n**3+2):
print(f'{n}\t{n**3+2}');
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Quackery
prime
is defined at Miller–Rabin primality test#Quackery.
[ dip number$
over size -
space swap of
swap join echo$ ] is recho ( n n --> )
199 times
[ i^ 1+ 3 ** 2 +
dup prime iff
[ i^ 1+ 4 recho
sp 7 recho cr ]
else drop ]
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Raku
# 20210315 Raku programming solution
say ((1…199)»³ »+»2).grep: *.is-prime
- Output:
(3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271)
REXX
Version 1
Since REXX doesn't have a isPrime function, this REXX program generates a number of primes such that some
numbers can be tested for primality directly, other numbers have to be tested by trial division for primality.
A suitable number was calculated to generate a number of primes such that about half of the computing time used to
test the numbers for primality could be directly determined their primality, the other half of the computing time used
would use trial division.
Since the task's requirements are pretty straight-forward and easy, a little extra code was added for presentation
(title and title separator line, the count of primes found, and commatization of the numbers).
/*REXX program finds and displays n primes of the form: n**3 + 2. */
parse arg LO HI hp . /*obtain optional argument from the CL.*/
if LO=='' | LO=="," then LO= 0 /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= 200 /* " " " " " " */
if hp=='' | hp=="," then hp= 19 /* " " " " " " */
h= max(iSqrt(HI**3), hp**3) /*a high prime to generate primes to. */
w= length( commas(HI**3) ) + 3
call genP /*build array of semaphores for primes.*/
say right('n', 20) ' (n**3 + 2)' /*display a title for the output list. */
say left('', 20 + w + 20, '─') /*display a sep for the output list. */
finds= 0 /*# of triplet strange primes (so far).*/
do j=LO+1 by 2 to HI-1 /*look for primes of form of: n**3 + 2 */
x= j**3 + 2
if x<=@.# then if \!.x then iterate /*Not a semaphore prime? Then skip it.*/
else nop /*the NOP matches up with the "THEN".*/
else do k=2 while @.k**2<=x /*perform a primality test by division.*/
if x//@.k==0 then iterate j
end /*k*/
finds= finds + 1 /*bump # primes found of form: n**3+2 */
say right(commas(j), 20) right( commas(x), w)
end /*j*/
say left('', 20 + w + 20, '─'); say /*display a sep for the output list. */
say 'Found ' commas(finds) ' primes in the form of: n**3 + 2'
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
iSqrt: procedure; parse arg x; r=0; q=1; do while q<=x; q=q*4; end
do while q>1; q=q%4; _=x-r-q; r=r%2; if _>=0 then do;x=_;r=r+q; end; end
return r
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0; pad= left('', 9) /*placeholders for primes; width of #'s*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; s.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ h. */
do j=@.#+2 by 2 to h /*find odd primes from here on. */
parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
/* [↑] the above five lines saves time*/
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return
- output when using the default inputs:
n (n**3 + 2) ──────────────────────────────────────────────────── 1 3 3 29 5 127 29 24,391 45 91,127 63 250,049 65 274,627 69 328,511 71 357,913 83 571,789 105 1,157,627 113 1,442,899 123 1,860,869 129 2,146,691 143 2,924,209 153 3,581,579 171 5,000,213 173 5,177,719 189 6,751,271 ──────────────────────────────────────────────────── Found 19 primes in the form of: n**3 + 2
Version 2
Libraries: How to use
Libraries: Source code
Prime(), the Miller-Rabin primality test, is in Numbers.
include Settings
say version; say 'Prime numbers of the form n^3+2'; say
numeric digits 44
say ' n n^3+2'
say '-----------'
n = 0
do i = 1 to 199
a = i*i*i+2
if IsPrime(a) then do
n = n+1
say Right(i,3) Right(a,7)
end
end
say '-----------'
say n 'primes found'
say Format(Time('e'),,3) 'seconds'; say
exit
include Functions
include Numbers
include Abend
- Output:
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024 Prime numbers of the form n^3+2 n n^3+2 ----------- 1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271 ----------- 19 primes found 0.006 seconds
Ring
load "stdlib.ring"
see "working..." + nl
for n = 1 to 200 step 2
pr = pow(n,3)+2
if isprime(pr)
see "n = " + n + " => n³+2 = " + pr + nl
ok
next
see "done..." + nl
- Output:
working... n = 1 => n³+2 = 3 n = 3 => n³+2 = 29 n = 5 => n³+2 = 127 n = 29 => n³+2 = 24391 n = 45 => n³+2 = 91127 n = 63 => n³+2 = 250049 n = 65 => n³+2 = 274627 n = 69 => n³+2 = 328511 n = 71 => n³+2 = 357913 n = 83 => n³+2 = 571789 n = 105 => n³+2 = 1157627 n = 113 => n³+2 = 1442899 n = 123 => n³+2 = 1860869 n = 129 => n³+2 = 2146691 n = 143 => n³+2 = 2924209 n = 153 => n³+2 = 3581579 n = 171 => n³+2 = 5000213 n = 173 => n³+2 = 5177719 n = 189 => n³+2 = 6751271 done...
RPL
≪ { }
1 200 FOR n
n 3 ^ 2 +
IF DUP ISPRIME? THEN + ELSE DROP END
NEXT
≫ 'TASK' STO
- Output:
1: {3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271}
Ruby
require 'prime'
p (1..200).filter_map{|n| cand = n**3 + 2; cand if cand.prime? }
- Output:
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]
Rust
// 202100327 Rust programming solution
use primes::is_prime;
fn main() {
let mut count = 0;
let begin = 0;
let end = 200;
println!("Find prime numbers of the form");
println!(" n => n³ + 2 ");
for n in begin+1..end-1 {
let m = n*n*n+2;
if is_prime(m) {
println!("{:4} => {}", n, m);
count += 1;
}
}
println!("Found {} such prime numbers where {} < n < {}.", count,begin,end);
}
- Output:
Find prime numbers of the form n => n³ + 2 1 => 3 3 => 29 5 => 127 29 => 24391 45 => 91127 63 => 250049 65 => 274627 69 => 328511 71 => 357913 83 => 571789 105 => 1157627 113 => 1442899 123 => 1860869 129 => 2146691 143 => 2924209 153 => 3581579 171 => 5000213 173 => 5177719 189 => 6751271 Found 19 such prime numbers where 0 < n < 200.
Seed7
Credit for isPrime
function: [1]
$ include "seed7_05.s7i";
const func boolean: isPrime (in integer: number) is func
result
var boolean: prime is FALSE;
local
var integer: upTo is 0;
var integer: testNum is 3;
begin
if number = 2 then
prime := TRUE;
elsif odd(number) and number > 2 then
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
testNum +:= 2;
end while;
prime := testNum > upTo;
end if;
end func;
const proc: main is func
local
const integer: limit is 199;
var integer: n is 1;
var integer: p is 0;
begin
writeln(" n n**3+2");
writeln("------------");
for n range 1 to limit step 2 do
p := n ** 3 + 2;
if isPrime(p) then
writeln(n lpad 3 <& p lpad 9);
end if;
end for;
end func;
- Output:
n n**3+2 ------------ 1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Sidef
1..^200 -> map { _**3 + 2 }.grep {.is_prime}.say
- Output:
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]
Swift
import Foundation
func isPrime(_ n: Int) -> Bool {
if n < 2 {
return false
}
if n % 2 == 0 {
return n == 2
}
if n % 3 == 0 {
return n == 3
}
var p = 5
while p * p <= n {
if n % p == 0 {
return false
}
p += 2
if n % p == 0 {
return false
}
p += 4
}
return true
}
for n in 1...200 {
let p = n * n * n + 2
if isPrime(p) {
print(String(format: "%3d%9d", n, p))
}
}
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
Verilog
module main;
function integer isPrime;
input integer ValorEval;
integer i;
integer prime;
begin
prime = 1; // We assume it is prime - Asumimos que es primo
if (ValorEval % 2 == 0) prime = 0;
else begin
i = 3;
while (i <= $sqrt(ValorEval) + 1) begin
if (ValorEval % i == 0) prime = 0;
i = i + 2;
end
end
isPrime = prime;
end
endfunction
integer n;
initial begin
for (n = 1; n <= 200; n = n + 1) begin
if (isPrime(n * n * n + 2)) $display("%d\t%d", n, n * n * n + 2);
end
end
endmodule
Wren
If n is even then n³ + 2 is also even, so we only need to examine odd values of n here.
import "./math" for Int
import "./iterate" for Stepped
import "./fmt" for Fmt
var limit = 200
for (n in Stepped.new(1...limit, 2)) {
var p = n*n*n + 2
if (Int.isPrime(p)) Fmt.print("n = $3d => n³ + 2 = $,9d", n, p)
}
- Output:
n = 1 => n³ + 2 = 3 n = 3 => n³ + 2 = 29 n = 5 => n³ + 2 = 127 n = 29 => n³ + 2 = 24,391 n = 45 => n³ + 2 = 91,127 n = 63 => n³ + 2 = 250,049 n = 65 => n³ + 2 = 274,627 n = 69 => n³ + 2 = 328,511 n = 71 => n³ + 2 = 357,913 n = 83 => n³ + 2 = 571,789 n = 105 => n³ + 2 = 1,157,627 n = 113 => n³ + 2 = 1,442,899 n = 123 => n³ + 2 = 1,860,869 n = 129 => n³ + 2 = 2,146,691 n = 143 => n³ + 2 = 2,924,209 n = 153 => n³ + 2 = 3,581,579 n = 171 => n³ + 2 = 5,000,213 n = 173 => n³ + 2 = 5,177,719 n = 189 => n³ + 2 = 6,751,271
XPL0
func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];
int N;
[for N:= 1 to 199 do
[if IsPrime(N*N*N+2) then
[IntOut(0, N);
ChOut(0, 9\tab\);
IntOut(0, N*N*N+2);
CrLf(0);
]
];
]
- Output:
1 3 3 29 5 127 29 24391 45 91127 63 250049 65 274627 69 328511 71 357913 83 571789 105 1157627 113 1442899 123 1860869 129 2146691 143 2924209 153 3581579 171 5000213 173 5177719 189 6751271
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