Step by Step solution about How to resolve the algorithm Wieferich primes step by step in the Go programming language

This code determines the Wieferich primes less than 5,000.

Wieferich Primes Wieferich primes are prime numbers (p) for which (2^{p-1}\equiv 1\pmod{p^2}). Another way to express this is that (p) divides (2^{p-1}-1).

Code Overview The code consists of three main parts:

1. Generating Primes:

   • The rcu.Primes(5000) function generates a slice of prime numbers less than 5,000.

2. Checking Wieferich Condition:

   • For each prime (p) in the slice:
     • Compute (2^{p-1} - 1) using the big.Int package.
     • Check if (p) divides the result by using num.Rem(num, den).Cmp(zero) == 0. If it does, it means (p) is a Wieferich prime.

3. Printing Results:

   • Iterate over the list of Wieferich primes and print each one using the rcu.Commatize function for readability.

Code Details

• big.Int Package: The program uses the big.Int package to handle large integer calculations.
• Commatize Function: The rcu.Commatize function is a helper function to add commas for readability to the prime numbers.
• fmt Package: The fmt package is used for input and output.

package main

import (
    "fmt"
    "math/big"
    "rcu"
)

func main() {
    primes := rcu.Primes(5000)
    zero := new(big.Int)
    one := big.NewInt(1)
    num := new(big.Int)
    fmt.Println("Wieferich primes < 5,000:")
    for _, p := range primes {
        num.Set(one)
        num.Lsh(num, uint(p-1))
        num.Sub(num, one)
        den := big.NewInt(int64(p * p))
        if num.Rem(num, den).Cmp(zero) == 0 {
            fmt.Println(rcu.Commatize(p))
        }
    }
}