A prime of the form 2n − 1 is called a Mersenne prime. (e) More generally, prove that if n is a composite number, then 2n − 1 is not prime. Thus, all Mersenne primes have the form 2p − 1 with p a prime number.

A prime of the form 2n − 1 is called a Mersenne prime. (e) More generally, prove that if n is a composite number, then 2n − 1 is not prime. Thus, all Mersenne primes have the form 2p − 1 with p a prime number.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A prime of the form 2ⁿ − 1 is called a Mersenne prime. (e) More generally, prove that if n is a composite number, then 2ⁿ − 1 is not prime. Thus, all Mersenne primes have the form 2^p − 1 with p a prime number.

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