Briana H.

asked • 12/07/12

Let p > 3 be a prime, and suppose that p = 3 (mod 4). If q = 2p+1 is also prime show that (2^p) -1 is never prime.

Need help with this promblem for number theory

Roman C.


I will try to figure this out for you. But my analysis of small cases suggests that p doesn't need to be prime.

As long as p = 3 mod 4 and q=2p+1 is prime, q will be a factor of 2p-1. Proving this would prove the conjecture because 2p+1 < 2p-1 when p>3.



1 Expert Answer


Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.


Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.