Gaussian primes: Difference between revisions

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=={{header|F_Sharp|F#}}==

This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]

<~~lang~~ fsharp>

// Gaussian primes. Nigel Galloway: July 29th., 2022

let isGP=function (n,0)|(0,n)->let n=abs n in n%4=3 && isPrime n |(n,g)->isPrime(n*n+g*g)

Seq.allPairs [-9..9] [-9..9]|>Seq.filter isGP|>Seq.iter(fun(n,g)->printf $"""%d{n}%s{match g with 0->"" |g->sprintf $"%+d{g}i"} """); printfn ""

</syntaxhighlight>

</lang>

<pre>

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</pre>

=={{header|J}}==

Implementation: <~~lang~~ J>isgpri=: {{

Implementation: <syntaxhighlight lang="j">isgpri=: {{

if. 1 p: (*+) y do. 1 return. end.

int=. |(+.y)-.0

if. 1=#int do. {.(1 p: int) * 3=4|int else. 0 end.

}}"0</~~lang~~>

}}"0</syntaxhighlight>

[https://jsoftware.github.io/j-playground/bin/html2/#code=isgpri%3D%3A%20%7B%7B%0A%20%20if.%201%20p%3A%20%28*%2B%29%20y%20do.%201%20return.%20end.%0A%20%20int%3D.%20%7C%28%2B.y%29-.0%0A%20%20if.%201%3D%23int%20do.%20%7B.%281%20p%3A%20int%29%20*%203%3D4%7Cint%20else.%200%20end.%0A%7D%7D%220%0A%0Arequire'viewmat'%0A%0Aviewmat%20%28isgpri%20*%20R%3E%3A%7C%29j.%2F~i%3AR%3D%3A%20100 Online plot of gaussian primes up to radius 100]. (Hit "Run" in the upper right-hand corner.)

Plot of gaussian primes up to radius 50: <~~lang~~ J> 1j1#"1'#' (<"1]50++.(#~ isgpri * 50>:|) ,j./~i:100)} '+' (<50 50)} '|' 50}"1 '-' 50} 100 100$' '</~~lang~~>

Plot of gaussian primes up to radius 50: <syntaxhighlight lang="j"> 1j1#"1'#' (<"1]50++.(#~ isgpri * 50>:|) ,j./~i:100)} '+' (<50 50)} '|' 50}"1 '-' 50} 100 100$' '</syntaxhighlight>

<pre style="font-size:60%;"> |

# # | # #

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</pre>

Gaussian primes less than radius 10 (sorted by radius):<~~lang~~ J> 10 10$(/: |)(#~ isgpri * 10>|) ,j./~i:10

Gaussian primes less than radius 10 (sorted by radius):<syntaxhighlight lang="j"> 10 10$(/: |)(#~ isgpri * 10>|) ,j./~i:10

_1j_1 _1j1 1j_1 1j1 _2j_1 _2j1 _1j_2 _1j2 1j_2 1j2

2j_1 2j1 _3 0j_3 0j3 3 _3j_2 _3j2 _2j_3 _2j3

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_5j_6 _5j6 5j_6 5j6 6j_5 6j5 _8j_3 _8j3 _3j_8 _3j8

3j_8 3j8 8j_3 8j3 _8j_5 _8j5 _5j_8 _5j8 5j_8 5j8

8j_5 8j5 _9j_4 _9j4 _4j_9 _4j9 4j_9 4j9 9j_4 9j4</~~lang~~>

8j_5 8j5 _9j_4 _9j4 _4j_9 _4j9 4j_9 4j9 9j_4 9j4</syntaxhighlight>

=={{header|Julia}}==

<~~lang~~ ruby>using LinearAlgebra

<syntaxhighlight lang="ruby">using LinearAlgebra

using Plots

using Primes

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testgaussprimes()

</~~lang~~>{{out}}

</syntaxhighlight>{{out}}

<pre>

Gaussian primes within 10 of the origin on the complex plane:

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=={{header|Mathematica}}/{{header|Wolfram Language}}==

<~~lang~~ ~~Mathematica~~>n = 100;

<syntaxhighlight lang="mathematica">n = 100;

digs = Reap@Do[If[Norm[i + I j]^2 < n, If[PrimeQ[i + I j, GaussianIntegers -> True], Sow[i + I j]]],

{i,Floor[-Sqrt[n]], Ceiling[Sqrt[n]]}, {j, Floor[-Sqrt[n]], Ceiling[Sqrt[n]]}

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digs //= Map[StringJoin];

digs //= StringRiffle[#, "\n"] &;

digs</~~lang~~>

digs</syntaxhighlight>

<pre>-9-4 I -9+4 I -8-5 I -8-3 I -8+3 I -8+5 I -7-2 I -7 -7+2 I -6-5 I

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=={{header|Perl}}==

<~~lang~~ perl>#!/usr/bin/perl

<syntaxhighlight lang="perl">#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Gaussian_primes

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}

return $plot, @primes;

}</~~lang~~>

}</syntaxhighlight>

<pre>Primes within 10

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You can run this online [http://phix.x10.mx/p2js/gp.htm here].

--

-- demo/rosetta/Gaussian_primes.exw

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IupClose()

end if

Output same as Raku

=={{header|Python}}==

<~~lang~~ python>''' python example for task rosettacode.org/wiki/Gaussian_primes '''

<syntaxhighlight lang="python">''' python example for task rosettacode.org/wiki/Gaussian_primes '''

from matplotlib.pyplot import scatter

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print(str(c).ljust(9), end='\n' if (i +1) % 10 == 0 else '')

scatter([c.real for c in gprimes], [c.imag for c in gprimes])

</~~lang~~>{{out}}

</syntaxhighlight>{{out}}

<pre>

Gaussian primes within 10 of the origin on the complex plane:

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=={{header|Raku}}==

Plotting the points up to a radius of 150.

<lang ~~perl6~~>use List::Divvy;

<syntaxhighlight lang="raku" line>use List::Divvy;

my @next = { :1x, :1y, :2n },;

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|@points

],

);</~~lang~~>

);</syntaxhighlight>

<pre>Gaussian primes with a norm less than 100 sorted by norm:

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Plots the points up to a radius of 150 to produce a similar image to the Raku example.

<~~lang~~ ecmascript>import "dome" for Window

<syntaxhighlight lang="ecmascript">import "dome" for Window

import "graphics" for Canvas, Color

import "./plot" for Axes

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}

var Game = Main.new()</~~lang~~>

var Game = Main.new()</syntaxhighlight>