Question

Never twin primes pair

Answer 1

Prove that for all \(n>2\) that \(2^n-1\) and \(2^n+1\) are never both prime at the same time.

Answer 2

Working mod 3 should help, I guess.

Answer 3

Yeah, you bet

Answer 4

I mean in mod 3, these guys can be written as \((-1)^n - 1\) and \((-1)^n +1\), and one of these has to be zero depending on the parity of \(n\).

Answer 5

That sounds right to me :D

Answer 6

Just a sorta interesting thing I came across while playing around with Mersenne primes and twin primes the other day, wanted to share, that's that haha.