(Mersenne prime) A prime number is called a Mersenne prime if it can be written in the form 2p - 1 for some positive integer p. Write a program that finds all Mersenne primes with p≤ 31 and displays the output as follows:

/*
(Mersenne prime) A prime number is called a Mersenne prime if it can be written
in the form 2p - 1 for some positive integer p. Write a program that finds all
Mersenne primes with p <= 31 and displays the output as follows:
p             2^p –1
-----------------------
2             3
3             7
5             31
...
*/
public class Exercise_06_28 {
	/** Main Method */
	public static void main(String[] args) {
		// Display table header
		System.out.println("\np           2^p-1");
		System.out.println("--------------------");

		// Display all Mersenne primes with p <= 31
		for (int p = 2; p <= 31; p++) {
			if (PrimeNumberMethod.isPrime(p)) {
				System.out.printf("%-13d", p);
				System.out.println(mersennePrime(p));
			}
		}
	}

	/** Method mersennePrime finds ans returns the mersenne prime of num*/
	public static int mersennePrime(int num) {
		return (int)Math.pow(2, num) - 1;
	}
}

PrimeNumberMethod.java

public class PrimeNumberMethod {
	public static void main(String[] args) {
		System.out.println("The first 50 prime numbers are \n");
		printPrimeNumbers(50);
	}

	public static void printPrimeNumbers(int numberOfPrimes) {
		final int NUMBER_OF_PRIMES_PER_LINE = 10; // Display 10 per line
		int count = 0; // Count the number of prime numbers
		int number = 2; // A number to be tested for primeness

		// Repeatedly find prime numbers
		while (count < numberOfPrimes) {
			// Print the prime number and increase the count
			if (isPrime(number)) {
				count++; // Increase the count
			
				if (count % NUMBER_OF_PRIMES_PER_LINE == 0) {
					// Print the number and advance to the new line
					System.out.printf("%-5s\n", number);
				}
				else
					System.out.printf("%-5s", number);
			}
	
			// Check whether the next number is prime
			number++;
		}
	}

	/** Check whether number is prime */
	public static boolean isPrime(int number) {
		for (int divisor = 2; divisor <= number/2; divisor++) {
			if (number % divisor == 0) { // If true, number is not prime
				return false; // Number is not a prime
			}
		}

		return true; // Number is prime
	}
}