Gaussian primes: Difference between revisions

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

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

// 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 ""

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<pre>

</pre>

=={{header|J}}==

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

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

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

 

[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.)

 

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

# # | # #

</pre>

 

_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

_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

 

=={{header|Julia}}==

using Plots

using Primes

 

testgaussprimes()

<pre>

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

 

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

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]]}

digs //= Map[StringJoin];

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

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<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

=={{header|Perl}}==

{{libheader|ntheory}}

 

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

}

return $plot, @primes;

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<pre>Primes within 10

{{libheader|Phix/online}}

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

<span style="color: #000080;font-style:italic;">--

-- demo/rosetta/Gaussian_primes.exw

<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

Output same as Raku

 

=={{header|Python}}==

 

from matplotlib.pyplot import scatter

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])

<pre>

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

=={{header|Raku}}==

Plotting the points up to a radius of 150.

 

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

|@points

],

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

{{libheader|wren-fmt}}

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

import "graphics" for Canvas, Color

import "./plot" for Axes

}

 

 

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