Chapter Sixth Chapter 28 (Mersenne prime) (Mersenne prime)

Chapter Sixth Chapter 28 (Mersenne prime) (Mersenne prime)

• **6.28 (Messen prime number) If a prime number can be written in the form of 2^p-1, where p is a positive integer, then this prime number is called a Mersenne prime number. Write a program to find all Mersenne prime numbers with p<=31, and then display the input results as follows:
  p 2^p-1
  2 3
  3 7
  5 31
  …
  **6.28(Mersenne prime) A prime number is called a Mersenne prime if it can be written in the form 2^p-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
  …
• Reference Code:

package chapter06;

public class Code_28 {
    
    
    public static void main(String[] args) {
    
    
        printTableHead();
        for(int i = 2;i <= 31;i++)
            if(isPrime((long)(Math.pow(2, i)-1)))
                System.out.printf("%d\t\t%d\n", i, (long)(Math.pow(2, i)-1));

    }
    public static boolean isPrime(long number) {
    
    
        for (int i = 2; i <= Math.sqrt(number); i++)
            if (number % i == 0)
                return false;
        return true;
    }
    public static void printTableHead() {
    
    
        System.out.println("p\t\t2^p-1");
        for(int i = 1;i <= 24;i++)
            System.out.print("-");
        System.out.print("\n");
    }
}

• The results show that:

p		2^p-1
------------------------
2		3
3		7
5		31
7		127
13		8191
17		131071
19		524287
31		2147483647

Process finished with exit code 0