How to resolve the algorithm Wilson primes of order n step by step in the J programming language

Published on 12 May 2024 09:40 PM
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How to resolve the algorithm Wilson primes of order n step by step in the J programming language

Table of Contents

Problem Statement

A Wilson prime of order n is a prime number   p   such that   p2   exactly divides:

If   n   is   1,   the latter formula reduces to the more familiar:   (p - n)! + 1   where the only known examples for   p   are   5,   13,   and   563.

Calculate and show on this page the Wilson primes, if any, for orders n = 1 to 11 inclusive and for primes p < 18   or, if your language supports big integers, for p < 11,000.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Wilson primes of order n step by step in the J programming language

Source code in the j programming language

   wilson=. 0 = (*:@] | _1&^@[ -~ -~ *&! <:@[)^:<:
   
   (>: i. 11x) ([ ;"0 wilson"0/ <@# ]) i.&.(p:inv) 11000
┌──┬───────────────┐
│1 │5 13 563       │
├──┼───────────────┤
│2 │2 3 11 107 4931│
├──┼───────────────┤
│3 │7              │
├──┼───────────────┤
│4 │10429          │
├──┼───────────────┤
│5 │5 7 47         │
├──┼───────────────┤
│6 │11             │
├──┼───────────────┤
│7 │17             │
├──┼───────────────┤
│8 │               │
├──┼───────────────┤
│9 │541            │
├──┼───────────────┤
│10│11 1109        │
├──┼───────────────┤
│11│17 2713        │
└──┴───────────────┘

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