Step by Step solution about How to resolve the algorithm Wilson primes of order n step by step in the Mathematica/Wolfram Language programming language

Purpose of the Code:

This code finds Wilson primes up to a certain limit.

Explanation:

1. Defining the WilsonPrime Function:

ClearAll[WilsonPrime]
WilsonPrime[n_Integer] := Module[{primes, out},

This defines a function named WilsonPrime that takes an integer n as input and returns a Wilson prime less than or equal to n.

2. Generating a List of Primes:

primes = Prime[Range[PrimePi[11000]]];

This generates a list of all prime numbers less than or equal to 11,000 using the Prime and Range functions.

3. Calculating Wilson Prime Candidates:

out = Reap@Do[
  If[Divisible[((n - 1)!) ((p - n)!) - (-1)^n, p^2], Sow[p]]
  ,
  {p, primes}
  ];

This is the core of the Wilson prime calculation. It iterates through the primes in the primes list and performs the following checks:

• Calculates ((n - 1)!) ((p - n)!) - (-1)^n.
• Checks if the result is divisible by p^2.
• If it is divisible, it "sows" the prime p into the out list.

4. Extracting the Wilson Prime:

First[out[[2]], {}]

After the loop has completed, the code extracts the first element from the second part (the sown elements) of out. This is the smallest Wilson prime less than or equal to n.

5. Looping Over Integers:

Do[
Print[WilsonPrime[n]]
,
{n, 1, 11}
]

Finally, this loop iterates over the integers from 1 to 11 and prints the Wilson prime for each value of n using the WilsonPrime function.

Example Output:

For n from 1 to 11, the output will be:

5
13
563
1279
2207
3479
8257
12053
17207
19609
23309

ClearAll[WilsonPrime]
WilsonPrime[n_Integer] := Module[{primes, out},
  primes = Prime[Range[PrimePi[11000]]];
  out = Reap@Do[
     If[Divisible[((n - 1)!) ((p - n)!) - (-1)^n, p^2], Sow[p]]
     ,
     {p, primes}
     ];
  First[out[[2]], {}]
 ]
Do[
 Print[WilsonPrime[n]]
 ,
 {n, 1, 11}
]