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

This Julia code efficiently generates and prints Wilson primes within a specified limit. Wilson primes are prime numbers p where (p-1)! ≡ -1 (mod p^2). The code leverages Julia's built-in Primes module for fast prime number generation.

1. Function Definition:

   • wilsonprimes(limit = 11000) defines a function that takes an optional limit as an argument and returns a list of Wilson primes within that limit.

2. Initialization:

   • Initialize sgn to 1 and facts as the product of integers from 1 to limit, stored as a big integer.
   • Print a header for the output.

3. Prime Generation and Checking:

   • Iterate through values of n from 1 to 11:

     • For each n, toggle the sign sgn to -1 or 1 to alternate the sign in the Wilson prime formula.

     • Iterate through prime numbers p up to the limit:

       • Check if p is greater than n and if the congruence (facts[n < 2 ? 1 : n - 1] * facts[p - n] - sgn) % p^2 == 0 holds. This checks if n is a Wilson prime for the current p.

       • If the congruence holds, print the prime p.

4. Output:

   • After iterating through all values of n, the list of Wilson primes is printed for each n.

using Primes

function wilsonprimes(limit = 11000)
    sgn, facts = 1, accumulate(*, 1:limit, init = big"1")
    println(" n:  Wilson primes\n--------------------")
    for n in 1:11
        print(lpad(n, 2), ":  ")
        sgn = -sgn
        for p in primes(limit)
            if p > n && (facts[n < 2 ? 1 : n - 1] * facts[p - n] - sgn) % p^2 == 0
                print("$p ")
            end
        end
        println()
    end
end

wilsonprimes()