Step by Step solution about How to resolve the algorithm Wagstaff primes step by step in the Java programming language

The provided Java code generates and prints prime numbers in the range 3 to 5808. It uses the BigInteger class to handle large integer values. A short explanation of the code:

• Generating primes:

  • The program starts by initializing a BigInteger d to 3 (a prime number) and lmt to 25 (the maximum number of digits to print).
  • It enters a loop that runs from i = 3 to 5808.
  • Inside the loop, it calculates a by shifting 1 by i bits to the left, adding 1, and dividing by d. This formula results in the next prime number after the current i.
  • If a is a probable prime (as determined by the isProbablePrime method with a certainty of 1), it's considered a prime.

• Printing primes:

  • The program prints the prime count c and the value of i (bit length) of the prime.
  • It then converts a to a String, calculates its length sl, and checks if sl is less than lmt.
  • If sl is less than lmt, it prints the entire prime. Otherwise, it prints only the first 11 and last 11 digits, along with the sl to indicate the total number of digits.

• Next probable prime:

  • After printing a prime, the program updates i to the next probable prime using the nextProbablePrime method of BigInteger. This method returns the next larger prime after i.

The program terminates after generating primes in the specified range.

import java.math.BigInteger; 

public class Main {
  public static void main(String[] args) {
    BigInteger d = new BigInteger("3"), a;
    int lmt = 25, sl, c = 0;
    for (int i = 3; i < 5808; ) {
      a = BigInteger.ONE.shiftLeft(i).add(BigInteger.ONE).divide(d);
      if (a.isProbablePrime(1)) {
        System.out.printf("%2d %4d ", ++c, i);
        String s = a.toString(); sl = s.length();
        if (sl < lmt) System.out.println(a);
        else System.out.println(s.substring(0, 11) + ".." + s.substring(sl - 11, sl) + " " + sl + " digits");
      }
      i = BigInteger.valueOf(i).nextProbablePrime().intValue();
    }
  }
}