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Find prime numbers of the form n*n*n+2: Difference between revisions

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Find prime numbers of the form n*n*n+2 (view source)

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;Task: Find prime numbers of the form &nbsp; <big> n<sup>''3''</sup>+2</big>, &nbsp; where 0 < n < 200
<br><br>
 
=={{header|11l}}==
{{trans|Python}}
 
<syntaxhighlight lang="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))
</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Ada}}==
<langsyntaxhighlight Adalang="ada">with Ada.Text_Io;
 
procedure Find_Primes is
Line 20 ⟶ 58:
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;
Line 45 ⟶ 83:
end if;
end loop;
end Find_Primes;</langsyntaxhighlight>
{{out}}
<pre> N N**3+2
Line 70 ⟶ 108:
 
=={{header|ALGOL 68}}==
<langsyntaxhighlight lang="algol68">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;
Line 84 ⟶ 122:
FI
OD
END</langsyntaxhighlight>
{{out}}
<pre>
Line 107 ⟶ 145:
189: 6751271
</pre>
 
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">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.</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Arturo}}==
<syntaxhighlight lang="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
]</syntaxhighlight>
 
{{out}}
 
<pre> 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</pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f FIND_PRIME_NUMBERS_OF_THE_FORM_NNN2.AWK
BEGIN {
Line 135 ⟶ 251:
return(1)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 162 ⟶ 278:
=={{header|C}}==
{{trans|Wren}}
<langsyntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
#include <locale.h>
Line 192 ⟶ 308:
}
return 0;
}</langsyntaxhighlight>
 
{{out}}
Line 218 ⟶ 334:
 
=={{header|C++}}==
<langsyntaxhighlight lang="cpp">#include <iomanip>
#include <iostream>
 
Line 244 ⟶ 360:
std::cout << std::setw(3) << n << std::setw(9) << p << '\n';
}
}</langsyntaxhighlight>
 
{{out}}
Line 268 ⟶ 384:
189 6751271
</pre>
 
=={{header|CLU}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|COBOL}}==
<syntaxhighlight lang="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.</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Cowgol}}==
<syntaxhighlight lang="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;</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{libheader| PrimTrial}}
<syntaxhighlight lang="delphi">
<lang Delphi>
program Find_prime_numbers_of_the_form_n_n_n_plus_2;
 
Line 300 ⟶ 621:
end;
readln;
end.</langsyntaxhighlight>
{{out}}
<pre>n = 1 => n^3 + 2 = 3
Line 321 ⟶ 642:
n = 173 => n^3 + 2 = 5,177,719
n = 189 => n^3 + 2 = 6,751,271</pre>
 
=={{header|Draco}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|EasyLang}}==
<syntaxhighlight>
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 & " "
.
.
</syntaxhighlight>
{{out}}
<pre>
3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271
</pre>
 
=={{header|F_Sharp|F#}}==
This task uses [[Extensible_prime_generator#The_functions|Extensible Prime Generator (F#)]].<br>
<langsyntaxhighlight lang="fsharp">
[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))
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 349 ⟶ 745:
n=189 -> 6751271
</pre>
 
=={{header|Factor}}==
Using the parity optimization from the Wren entry:
{{works with|Factor|0.99 2021-02-05}}
<langsyntaxhighlight lang="factor">USING: formatting kernel math math.functions math.primes
math.ranges sequences tools.memory.private ;
 
Line 358 ⟶ 755:
dup 3 ^ 2 + dup prime?
[ commas "n = %3d => n³ + 2 = %9s\n" printf ] [ 2drop ] if
] each</langsyntaxhighlight>
Or, using local variables:
{{trans|Wren}}
{{works with|Factor|0.99 2021-02-05}}
<langsyntaxhighlight lang="factor">USING: formatting kernel math math.primes math.ranges sequences
tools.memory.private ;
 
Line 372 ⟶ 769:
[ n p commas "n = %3d => n³ + 2 = %9s\n" printf ] when
] each
]</langsyntaxhighlight>
{{out}}
<pre>
Line 397 ⟶ 794:
 
=={{header|Fermat}}==
<langsyntaxhighlight lang="fermat">for n=1,199 do if Isprime(n^3+2)=1 then !!(n,n^3+2) fi od</langsyntaxhighlight>
{{out}}
<pre>
Line 423 ⟶ 820:
=={{header|Forth}}==
{{works with|Gforth}}
<langsyntaxhighlight lang="forth">: prime? ( n -- flag )
dup 2 < if drop false exit then
dup 2 mod 0= if 2 = exit then
Line 448 ⟶ 845:
 
main
bye</langsyntaxhighlight>
 
{{out}}
Line 475 ⟶ 872:
=={{header|FreeBASIC}}==
Use the code from [[Primality by trial division#FreeBASIC]] as an include.
<langsyntaxhighlight lang="freebasic">#include"isprime.bas"
 
for n as uinteger = 1 to 200
Line 481 ⟶ 878:
print n, n^3+2
end if
next n</langsyntaxhighlight>
{{out}}
<pre>
Line 504 ⟶ 901:
189 6751271
</pre>
 
=={{header|Frink}}==
<syntaxhighlight lang="frink">for n = 1 to 199
if isPrime[n^3 + 2]
println["$n\t" + n^3+2]</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Fōrmulæ}}==
 
{{FormulaeEntry|page=https://formulae.org/?script=examples/Find_prime_numbers_of_the_form_n%C2%B3%2B2}}
 
'''Solution'''
 
[[File:Fōrmulæ - Find prime numbers of the form n³ + 2 01.png]]
 
[[File:Fōrmulæ - Find prime numbers of the form n³ + 2 02.png]]
 
=={{header|Go}}==
<langsyntaxhighlight lang="go">package main
 
import "fmt"
Line 557 ⟶ 991:
}
}
}</langsyntaxhighlight>
 
{{out}}
Line 580 ⟶ 1,014:
n = 173 => n³ + 2 = 5,177,719
n = 189 => n³ + 2 = 6,751,271
</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j">([,.2+]^3:)@([#~1:p:2+]^3:) }.i.200x</syntaxhighlight>
{{out}}
<pre> 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</pre>
 
=={{header|jq}}==
{{works with|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]]:
<syntaxhighlight lang="jq">
range(1;200) | pow(.; 3) + 2 | select(is_prime)
</syntaxhighlight>
{{out}}
<pre>
3
29
127
24391
91127
250049
274627
328511
357913
571789
1157627
1442899
1860869
2146691
2924209
3581579
5000213
5177719
6751271
</pre>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia"># Formatting output as in Go example.
using Primes, Formatting
 
Line 604 ⟶ 1,093:
 
filterprintresults(isncubedplus2prime, 0, 200, tostring)
</langsyntaxhighlight>{{out}}
<pre>
n = 1 => n³ + 2 = 3
Line 629 ⟶ 1,118:
</pre>
=== One-liner version ===
<langsyntaxhighlight lang="julia">using Primes; println(filter(isprime, map(x -> x^3 + 2, 1:199)))</langsyntaxhighlight>{{out}}<pre>
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]</pre>
 
=={{header|MAD}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Select[Range[199]^3 + 2, PrimeQ]</syntaxhighlight>
{{out}}
<pre>{3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271}</pre>
 
=={{header|Nim}}==
<syntaxhighlight lang="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</syntaxhighlight>
 
{{out}}
<pre> 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</pre>
 
=={{header|PARI/GP}}==
<langsyntaxhighlight lang="parigp">for(N=1,200,if(isprime(N^3+2),print(N," ",N^3+2)))</langsyntaxhighlight>
{{out}}
<pre>
Line 655 ⟶ 1,239:
173 5177719
189 6751271
</pre>
 
=={{header|Pascal}}==
==={{header|Free Pascal}}===
{{trans|Delphi}}
{{libheader| PrimTrial}}
<syntaxhighlight lang="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.</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Perl}}==
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
Line 674 ⟶ 1,354:
}
print "\n";
}</langsyntaxhighlight>
 
{{out}}
Line 693 ⟶ 1,373:
 
=={{header|Phix}}==
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">pn3p2</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: #004080;">integer</span> <span style="color: #000000;">n3p2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">2</span>
Line 701 ⟶ 1,381:
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Found %d primes of the form n^3+2:\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">printf</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"n = %3d =&gt; n^3+2 = %,9d\n"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
Line 727 ⟶ 1,407:
 
=={{header|Plain English}}==
<langsyntaxhighlight lang="plainenglish">To run:
Start up.
Put 1 into a counter.
Line 740 ⟶ 1,420:
Write "Done." on the console.
Wait for the escape key.
Shut down.</langsyntaxhighlight>
{{out}}
<pre>
Line 763 ⟶ 1,443:
189 6751271
Done.
</pre>
 
 
=={{header|Python}}==
<syntaxhighlight lang="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}');</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Quackery}}==
 
<code>prime</code> is defined at [[Miller–Rabin primality test#Quackery]].
 
<syntaxhighlight lang="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 ]</syntaxhighlight>
 
{{out}}
 
<pre> 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
</pre>
 
=={{header|Raku}}==
<syntaxhighlight lang="raku" perl6line># 20210315 Raku programming solution
 
say ((1…199)»³ »+»2).grep: *.is-prime</langsyntaxhighlight>
{{out}}
<pre>
Line 783 ⟶ 1,537:
Since the task's requirements are pretty straight-forward and easy, &nbsp; a little extra code was added for presentation
<br>(title and title separator line, &nbsp; the count of primes found, &nbsp; and commatization of the numbers).
<langsyntaxhighlight lang="rexx">/*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.*/
Line 830 ⟶ 1,584:
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
Line 860 ⟶ 1,614:
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
load "stdlib.ring"
 
Line 873 ⟶ 1,627:
 
see "done..." + nl
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 899 ⟶ 1,653:
 
</pre>
 
=={{header|RPL}}==
{{works with|HP|49g}}
≪ { }
1 200 '''FOR''' n
n 3 ^ 2 +
'''IF''' DUP ISPRIME? '''THEN''' + '''ELSE''' DROP '''END'''
'''NEXT'''
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271}
</pre>
 
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
p (1..200).filter_map{|n| cand = n**3 + 2; cand if cand.prime? }
</syntaxhighlight>
{{out}}
<pre>[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]</pre>
 
=={{header|Rust}}==
<langsyntaxhighlight lang="rust">// 202100327 Rust programming solution
 
use primes::is_prime;
Line 923 ⟶ 1,697:
 
println!("Found {} such prime numbers where {} < n < {}.", count,begin,end);
}</langsyntaxhighlight>
{{out}}
<pre>
Line 952 ⟶ 1,726:
=={{header|Seed7}}==
Credit for <code>isPrime</code> function: [http://seed7.sourceforge.net/algorith/math.htm#isPrime]
<langsyntaxhighlight lang="seed7">$ include "seed7_05.s7i";
 
const func boolean: isPrime (in integer: number) is func
Line 986 ⟶ 1,760:
end if;
end for;
end func;</langsyntaxhighlight>
{{out}}
<pre>
Line 1,010 ⟶ 1,784:
173 5177719
189 6751271
</pre>
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">1..^200 -> map { _**3 + 2 }.grep {.is_prime}.say</syntaxhighlight>
{{out}}
<pre>
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]
</pre>
 
=={{header|Swift}}==
<langsyntaxhighlight lang="swift">import Foundation
 
func isPrime(_ n: Int) -> Bool {
Line 1,044 ⟶ 1,825:
print(String(format: "%3d%9d", n, p))
}
}</langsyntaxhighlight>
 
{{out}}
Line 1,071 ⟶ 1,852:
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-traititerate}}
{{libheader|Wren-fmt}}
If ''n'' is even then ''n³ + 2'' is also even, so we only need to examine odd values of ''n'' here.
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Int
import "./traititerate" for Stepped
import "./fmt" for Fmt
 
var limit = 200
Line 1,082 ⟶ 1,863:
var p = n*n*n + 2
if (Int.isPrime(p)) Fmt.print("n = $3d => n³ + 2 = $,9d", n, p)
}</langsyntaxhighlight>
 
{{out}}
Line 1,108 ⟶ 1,889:
 
=={{header|XPL0}}==
<langsyntaxhighlight XPL0lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
Line 1,125 ⟶ 1,906:
]
];
]</langsyntaxhighlight>
 
{{out}}
Chkas
1,973

edits

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