Q.1
If we let x = 5 in the Mersenne Number formula, is the result prime or composite?
2^5 - 1 = 31, which is prime because it only has two factors, 1 and 31.
2^5 - 1 = 9, which is not prime because it has more than two factors, 1, 3, 9.
2^5 - 1 = 32, which is not prime because it has more than two factors, 1, 2, 4, 8, 16 and 32.
Q.2
If we let x = 6 in the Mersenne Number formula, is the result prime or composite?
2^6 - 1 = 63, which is prime because it only has two factors, 1 and 63.
2^6 - 1 = 63, which is not prime because it has more than 2 factors: it is divisible by 1, 3, 7, 9, and 63.
2^6 - 1 = 11, which is prime because it only has two factors, 1 and 11.