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

Content added Content deleted
m (Ada: Fix Is_Prime)
m (syntax highlighting fixup automation)
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=={{header|Ada}}==
=={{header|Ada}}==
<lang Ada>with Ada.Text_Io;
<syntaxhighlight lang="ada">with Ada.Text_Io;


procedure Find_Primes is
procedure Find_Primes is
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end if;
end if;
end loop;
end loop;
end Find_Primes;</lang>
end Find_Primes;</syntaxhighlight>
{{out}}
{{out}}
<pre> N N**3+2
<pre> N N**3+2
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=={{header|ALGOL 68}}==
=={{header|ALGOL 68}}==
<lang algol68>BEGIN # Find n such that n^3 + 2 is a prime for n < 200 #
<syntaxhighlight lang="algol68">BEGIN # Find n such that n^3 + 2 is a prime for n < 200 #
FOR n TO 199 DO
FOR n TO 199 DO
INT candidate = ( n * n * n ) + 2;
INT candidate = ( n * n * n ) + 2;
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FI
FI
OD
OD
END</lang>
END</syntaxhighlight>
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<pre>
<pre>
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=={{header|ALGOL W}}==
=={{header|ALGOL W}}==
<lang algolw>begin % Find n such that n^3 + 2 is a prime for n < 200 %
<syntaxhighlight lang="algolw">begin % Find n such that n^3 + 2 is a prime for n < 200 %
for n := 1 until 199 do begin
for n := 1 until 199 do begin
integer candidate;
integer candidate;
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end if_isPrime
end if_isPrime
end for_n
end for_n
end.</lang>
end.</syntaxhighlight>
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<pre>
<pre>
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=={{header|AWK}}==
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f FIND_PRIME_NUMBERS_OF_THE_FORM_NNN2.AWK
# syntax: GAWK -f FIND_PRIME_NUMBERS_OF_THE_FORM_NNN2.AWK
BEGIN {
BEGIN {
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return(1)
return(1)
}
}
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
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=={{header|C}}==
=={{header|C}}==
{{trans|Wren}}
{{trans|Wren}}
<lang c>#include <stdio.h>
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
#include <stdbool.h>
#include <locale.h>
#include <locale.h>
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}
}
return 0;
return 0;
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
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=={{header|C++}}==
=={{header|C++}}==
<lang cpp>#include <iomanip>
<syntaxhighlight lang="cpp">#include <iomanip>
#include <iostream>
#include <iostream>


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std::cout << std::setw(3) << n << std::setw(9) << p << '\n';
std::cout << std::setw(3) << n << std::setw(9) << p << '\n';
}
}
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
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=={{header|CLU}}==
=={{header|CLU}}==
<lang clu>is_prime = proc (n: int) returns (bool)
<syntaxhighlight lang="clu">is_prime = proc (n: int) returns (bool)
if n<2 then return(false) end
if n<2 then return(false) end
if n//2=0 then return(n=2) end
if n//2=0 then return(n=2) end
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stream$putl(po, "")
stream$putl(po, "")
end
end
end start_up</lang>
end start_up</syntaxhighlight>
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{{out}}
<pre>n = 1 => n^3 + 2 = 3
<pre>n = 1 => n^3 + 2 = 3
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=={{header|COBOL}}==
=={{header|COBOL}}==
<lang cobol> IDENTIFICATION DIVISION.
<syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION.
PROGRAM-ID. N3-PLUS-2-PRIMES.
PROGRAM-ID. N3-PLUS-2-PRIMES.
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CHECK-PRIME-DONE.
CHECK-PRIME-DONE.
EXIT.</lang>
EXIT.</syntaxhighlight>
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{{out}}
<pre>N = 1 => N ** 3 + 2 = 3
<pre>N = 1 => N ** 3 + 2 = 3
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=={{header|Cowgol}}==
=={{header|Cowgol}}==
<lang cowgol>include "cowgol.coh";
<syntaxhighlight lang="cowgol">include "cowgol.coh";


sub is_prime(n: uint32): (p: uint8) is
sub is_prime(n: uint32): (p: uint8) is
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end if;
end if;
n := n+1;
n := n+1;
end loop;</lang>
end loop;</syntaxhighlight>
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<pre>n = 1 => n^3 + 2 = 3
<pre>n = 1 => n^3 + 2 = 3
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{{libheader| System.SysUtils}}
{{libheader| System.SysUtils}}
{{libheader| PrimTrial}}
{{libheader| PrimTrial}}
<syntaxhighlight lang="delphi">
<lang Delphi>
program Find_prime_numbers_of_the_form_n_n_n_plus_2;
program Find_prime_numbers_of_the_form_n_n_n_plus_2;


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end;
end;
readln;
readln;
end.</lang>
end.</syntaxhighlight>
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<pre>n = 1 => n^3 + 2 = 3
<pre>n = 1 => n^3 + 2 = 3
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=={{header|F_Sharp|F#}}==
=={{header|F_Sharp|F#}}==
This task uses [[Extensible_prime_generator#The_functions|Extensible Prime Generator (F#)]].<br>
This task uses [[Extensible_prime_generator#The_functions|Extensible Prime Generator (F#)]].<br>
<lang fsharp>
<syntaxhighlight 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))
[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>
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<pre>
<pre>
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Using the parity optimization from the Wren entry:
Using the parity optimization from the Wren entry:
{{works with|Factor|0.99 2021-02-05}}
{{works with|Factor|0.99 2021-02-05}}
<lang factor>USING: formatting kernel math math.functions math.primes
<syntaxhighlight lang="factor">USING: formatting kernel math math.functions math.primes
math.ranges sequences tools.memory.private ;
math.ranges sequences tools.memory.private ;


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dup 3 ^ 2 + dup prime?
dup 3 ^ 2 + dup prime?
[ commas "n = %3d => n³ + 2 = %9s\n" printf ] [ 2drop ] if
[ commas "n = %3d => n³ + 2 = %9s\n" printf ] [ 2drop ] if
] each</lang>
] each</syntaxhighlight>
Or, using local variables:
Or, using local variables:
{{trans|Wren}}
{{trans|Wren}}
{{works with|Factor|0.99 2021-02-05}}
{{works with|Factor|0.99 2021-02-05}}
<lang factor>USING: formatting kernel math math.primes math.ranges sequences
<syntaxhighlight lang="factor">USING: formatting kernel math math.primes math.ranges sequences
tools.memory.private ;
tools.memory.private ;


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[ n p commas "n = %3d => n³ + 2 = %9s\n" printf ] when
[ n p commas "n = %3d => n³ + 2 = %9s\n" printf ] when
] each
] each
]</lang>
]</syntaxhighlight>
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<pre>
<pre>
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=={{header|Fermat}}==
=={{header|Fermat}}==
<lang fermat>for n=1,199 do if Isprime(n^3+2)=1 then !!(n,n^3+2) fi od</lang>
<syntaxhighlight lang="fermat">for n=1,199 do if Isprime(n^3+2)=1 then !!(n,n^3+2) fi od</syntaxhighlight>
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<pre>
<pre>
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=={{header|Forth}}==
=={{header|Forth}}==
{{works with|Gforth}}
{{works with|Gforth}}
<lang forth>: prime? ( n -- flag )
<syntaxhighlight lang="forth">: prime? ( n -- flag )
dup 2 < if drop false exit then
dup 2 < if drop false exit then
dup 2 mod 0= if 2 = exit then
dup 2 mod 0= if 2 = exit then
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main
main
bye</lang>
bye</syntaxhighlight>


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=={{header|FreeBASIC}}==
=={{header|FreeBASIC}}==
Use the code from [[Primality by trial division#FreeBASIC]] as an include.
Use the code from [[Primality by trial division#FreeBASIC]] as an include.
<lang freebasic>#include"isprime.bas"
<syntaxhighlight lang="freebasic">#include"isprime.bas"


for n as uinteger = 1 to 200
for n as uinteger = 1 to 200
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print n, n^3+2
print n, n^3+2
end if
end if
next n</lang>
next n</syntaxhighlight>
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<pre>
<pre>
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=={{header|Frink}}==
=={{header|Frink}}==
<lang frink>for n = 1 to 199
<syntaxhighlight lang="frink">for n = 1 to 199
if isPrime[n^3 + 2]
if isPrime[n^3 + 2]
println["$n\t" + n^3+2]</lang>
println["$n\t" + n^3+2]</syntaxhighlight>
{{out}}
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<pre>
<pre>
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=={{header|Go}}==
=={{header|Go}}==
<lang go>package main
<syntaxhighlight lang="go">package main


import "fmt"
import "fmt"
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}
}
}
}
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
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=={{header|J}}==
=={{header|J}}==
<lang j>([,.2+]^3:)@([#~1:p:2+]^3:) }.i.200x</lang>
<syntaxhighlight lang="j">([,.2+]^3:)@([#~1:p:2+]^3:) }.i.200x</syntaxhighlight>
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<pre> 1 3
<pre> 1 3
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Using a definition of `is_prime` such as can be found at
Using a definition of `is_prime` such as can be found at
[[Safe_primes_and_unsafe_primes]]:
[[Safe_primes_and_unsafe_primes]]:
<syntaxhighlight lang="jq">
<lang jq>
range(1;200) | pow(.; 3) + 2 | select(is_prime)
range(1;200) | pow(.; 3) + 2 | select(is_prime)
</syntaxhighlight>
</lang>
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<pre>
<pre>
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=={{header|Julia}}==
=={{header|Julia}}==
<lang julia># Formatting output as in Go example.
<syntaxhighlight lang="julia"># Formatting output as in Go example.
using Primes, Formatting
using Primes, Formatting


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filterprintresults(isncubedplus2prime, 0, 200, tostring)
filterprintresults(isncubedplus2prime, 0, 200, tostring)
</lang>{{out}}
</syntaxhighlight>{{out}}
<pre>
<pre>
n = 1 => n³ + 2 = 3
n = 1 => n³ + 2 = 3
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</pre>
</pre>
=== One-liner version ===
=== One-liner version ===
<lang julia>using Primes; println(filter(isprime, map(x -> x^3 + 2, 1:199)))</lang>{{out}}<pre>
<syntaxhighlight lang="julia">using Primes; println(filter(isprime, map(x -> x^3 + 2, 1:199)))</syntaxhighlight>{{out}}<pre>
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]</pre>
[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]</pre>


=={{header|MAD}}==
=={{header|MAD}}==
<lang mad> NORMAL MODE IS INTEGER
<syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER
INTERNAL FUNCTION(P)
INTERNAL FUNCTION(P)
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END OF CONDITIONAL
END OF CONDITIONAL
LOOP CONTINUE
LOOP CONTINUE
END OF PROGRAM</lang>
END OF PROGRAM</syntaxhighlight>
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<pre>N = 1 N*N*N + 2 = 3
<pre>N = 1 N*N*N + 2 = 3
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<lang Mathematica>Select[Range[199]^3 + 2, PrimeQ]</lang>
<syntaxhighlight lang="mathematica">Select[Range[199]^3 + 2, PrimeQ]</syntaxhighlight>
{{out}}
{{out}}
<pre>{3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271}</pre>
<pre>{3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271}</pre>


=={{header|Nim}}==
=={{header|Nim}}==
<lang Nim>import strutils
<syntaxhighlight lang="nim">import strutils


func isPrime(n: Positive): bool =
func isPrime(n: Positive): bool =
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let p = n * n * n + 2
let p = n * n * n + 2
if p.isPrime:
if p.isPrime:
echo ($n).align(3), " → ", p</lang>
echo ($n).align(3), " → ", p</syntaxhighlight>


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=={{header|PARI/GP}}==
=={{header|PARI/GP}}==
<lang parigp>for(N=1,200,if(isprime(N^3+2),print(N," ",N^3+2)))</lang>
<syntaxhighlight lang="parigp">for(N=1,200,if(isprime(N^3+2),print(N," ",N^3+2)))</syntaxhighlight>
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<pre>
<pre>
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=={{header|Perl}}==
=={{header|Perl}}==
<lang perl>use strict;
<syntaxhighlight lang="perl">use strict;
use warnings;
use warnings;
use feature 'say';
use feature 'say';
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}
}
print "\n";
print "\n";
}</lang>
}</syntaxhighlight>


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=={{header|Phix}}==
=={{header|Phix}}==
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="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: #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>
<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>
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<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;">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>
<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>
<!--</lang>-->
<!--</syntaxhighlight>-->
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<pre>
<pre>
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=={{header|Plain English}}==
=={{header|Plain English}}==
<lang plainenglish>To run:
<syntaxhighlight lang="plainenglish">To run:
Start up.
Start up.
Put 1 into a counter.
Put 1 into a counter.
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Write "Done." on the console.
Write "Done." on the console.
Wait for the escape key.
Wait for the escape key.
Shut down.</lang>
Shut down.</syntaxhighlight>
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<pre>
<pre>
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=={{header|Python}}==
=={{header|Python}}==
<lang python>#!/usr/bin/python
<syntaxhighlight lang="python">#!/usr/bin/python


def isPrime(n):
def isPrime(n):
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for n in range(1, 200):
for n in range(1, 200):
if isPrime(n**3+2):
if isPrime(n**3+2):
print(f'{n}\t{n**3+2}');</lang>
print(f'{n}\t{n**3+2}');</syntaxhighlight>
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<pre>1 3
<pre>1 3
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=={{header|Raku}}==
=={{header|Raku}}==
<lang perl6># 20210315 Raku programming solution
<syntaxhighlight lang="raku" line># 20210315 Raku programming solution


say ((1…199)»³ »+»2).grep: *.is-prime</lang>
say ((1…199)»³ »+»2).grep: *.is-prime</syntaxhighlight>
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<pre>
<pre>
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Since the task's requirements are pretty straight-forward and easy, &nbsp; a little extra code was added for presentation
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).
<br>(title and title separator line, &nbsp; the count of primes found, &nbsp; and commatization of the numbers).
<lang rexx>/*REXX program finds and displays n primes of the form: n**3 + 2. */
<syntaxhighlight 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.*/
parse arg LO HI hp . /*obtain optional argument from the CL.*/
if LO=='' | LO=="," then LO= 0 /*Not specified? Then use the default.*/
if LO=='' | LO=="," then LO= 0 /*Not specified? Then use the default.*/
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end /*k*/ /* [↑] only process numbers ≤ √ J */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</lang>
end /*j*/; return</syntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
<pre>
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=={{header|Ring}}==
=={{header|Ring}}==
<lang ring>
<syntaxhighlight lang="ring">
load "stdlib.ring"
load "stdlib.ring"


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see "done..." + nl
see "done..." + nl
</syntaxhighlight>
</lang>
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<pre>
<pre>
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=={{header|Rust}}==
=={{header|Rust}}==
<lang rust>// 202100327 Rust programming solution
<syntaxhighlight lang="rust">// 202100327 Rust programming solution


use primes::is_prime;
use primes::is_prime;
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println!("Found {} such prime numbers where {} < n < {}.", count,begin,end);
println!("Found {} such prime numbers where {} < n < {}.", count,begin,end);
}</lang>
}</syntaxhighlight>
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<pre>
<pre>
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=={{header|Seed7}}==
=={{header|Seed7}}==
Credit for <code>isPrime</code> function: [http://seed7.sourceforge.net/algorith/math.htm#isPrime]
Credit for <code>isPrime</code> function: [http://seed7.sourceforge.net/algorith/math.htm#isPrime]
<lang seed7>$ include "seed7_05.s7i";
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";


const func boolean: isPrime (in integer: number) is func
const func boolean: isPrime (in integer: number) is func
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end if;
end if;
end for;
end for;
end func;</lang>
end func;</syntaxhighlight>
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<pre>
<pre>
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=={{header|Sidef}}==
=={{header|Sidef}}==
<lang ruby>1..^200 -> map { _**3 + 2 }.grep {.is_prime}.say</lang>
<syntaxhighlight lang="ruby">1..^200 -> map { _**3 + 2 }.grep {.is_prime}.say</syntaxhighlight>
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<pre>
<pre>
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=={{header|Swift}}==
=={{header|Swift}}==
<lang swift>import Foundation
<syntaxhighlight lang="swift">import Foundation


func isPrime(_ n: Int) -> Bool {
func isPrime(_ n: Int) -> Bool {
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print(String(format: "%3d%9d", n, p))
print(String(format: "%3d%9d", n, p))
}
}
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
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{{libheader|Wren-fmt}}
{{libheader|Wren-fmt}}
If ''n'' is even then ''n³ + 2'' is also even, so we only need to examine odd values of ''n'' here.
If ''n'' is even then ''n³ + 2'' is also even, so we only need to examine odd values of ''n'' here.
<lang ecmascript>import "/math" for Int
<syntaxhighlight lang="ecmascript">import "/math" for Int
import "/trait" for Stepped
import "/trait" for Stepped
import "/fmt" for Fmt
import "/fmt" for Fmt
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var p = n*n*n + 2
var p = n*n*n + 2
if (Int.isPrime(p)) Fmt.print("n = $3d => n³ + 2 = $,9d", n, p)
if (Int.isPrime(p)) Fmt.print("n = $3d => n³ + 2 = $,9d", n, p)
}</lang>
}</syntaxhighlight>


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=={{header|XPL0}}==
=={{header|XPL0}}==
<lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number
<syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
int N, I;
[if N <= 1 then return false;
[if N <= 1 then return false;
Line 1,601: Line 1,601:
]
]
];
];
]</lang>
]</syntaxhighlight>


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