A Mersenne number is an Integer of the form 2p 1 where p Is

A Mersenne number is an Integer of the form 2^p -1. where p Is a prime. For example, the first three Mersenne numbers are 3, 7, and 31 (for p = 2, 3. and 5, respectively!. By examining the first six Mersenne numbers (for p - 2, 3, 5, 7, 11, 13). show that 2^p - 1 can be composite but may be prime-even when p is a prime - even when p is a prime.

Solution

by examining the sequence

2^2 -1 =3

2^3 -1 = 7

2^5 -1=31

2^7 -1 = 127

2^11 -1 =2047

2^13 -1 = 8191

2047 is not aprime number, can b factorizwd as 23*89 =2047

So Meresenne number can be composite even when p is prime.but may be prime in most cases