Mersenne Prime | Program to generate mersenne primes ; Generate all prime numbers less than n . ; Initialize all entries of boolean array as true . A value in prime [ i ] will finally be false if i is Not a prime , else true bool prime [ n + 1 ] ; ; If prime [ p ] is not changed , then it is a prime ; Update all multiples of p ; Function to generate mersenne primes less than or equal to n ; Create a boolean array " prime [ 0 . . n ] " ; Generating primes using Sieve ; Generate all numbers of the form 2 ^ k - 1 and smaller than or equal to n . ; Checking whether number is prime and is one less then the power of 2 ; Driven program
#include <bits/stdc++.h> NEW_LINE using namespace std ; void SieveOfEratosthenes ( int n , bool prime [ ] ) { for ( int i = 0 ; i <= n ; i ++ ) prime [ i ] = true ; for ( int p = 2 ; p * p <= n ; p ++ ) { if ( prime [ p ] == true ) { for ( int i = p * 2 ; i <= n ; i += p ) prime [ i ] = false ; } } } void mersennePrimes ( int n ) { bool prime [ n + 1 ] ; SieveOfEratosthenes ( n , prime ) ; for ( int k = 2 ; ( ( 1 << k ) - 1 ) <= n ; k ++ ) { long long num = ( 1 << k ) - 1 ; if ( prime [ num ] ) cout << num << " ▁ " ; } } int main ( ) { int n = 31 ; cout << " Mersenne ▁ prime ▁ numbers ▁ smaller ▁ " << " than ▁ or ▁ equal ▁ to ▁ " << n << endl ; mersennePrimes ( n ) ; return 0 ; }