How to resolve the algorithm Primality by Wilson's theorem step by step in the Raku programming language

Published on 12 May 2024 09:40 PM
#Raku

How to resolve the algorithm Primality by Wilson's theorem step by step in the Raku programming language

Table of Contents

Problem Statement

Write a boolean function that tells whether a given integer is prime using Wilson's theorem. By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1. Remember that 1 and all non-positive integers are not prime.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Primality by Wilson's theorem step by step in the Raku programming language

Source code in the raku programming language

sub postfix: (Int $n) { (constant f = 1, |[\*] 1..*)[$n] }

sub is-wilson-prime (Int $p where * > 1) { (($p - 1)! + 1) %% $p }

# Pre initialize factorial routine (not thread safe)
9000!;

# Testing
put '   p  prime?';
printf("%4d  %s\n", $_, .&is-wilson-prime) for 2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659;

my $wilsons = (2,3,*+2…*).hyper.grep: &is-wilson-prime;

put "\nFirst 120 primes:";
put $wilsons[^120].rotor(20)».fmt('%3d').join: "\n";

put "\n1000th through 1015th primes:";
put $wilsons[999..1014];

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