Talk:Mersenne conjectures

This sentence makes no sense to me: "However, according to Robert D. Silverman, John Selfridge agreed that the New Mersenne conjecture is "obviously true" as it was chosen to fit the known data and counter-examples beyond those cases are exceedingly unlikely. It may be regarded more as a curious observation than as an open question in need of proving." How can it be "obviously true" if people can't figure out how to prove it? That's like saying the twin prime conjecture is "obviously true" because for 99.9% of the twin primes we've found, there is a larger pair. —Preceding unsigned comment added by 75.22.30.187 (talk • contribs)

I share your doubts about the sentence you quote. If there is no one to defend it, it should go.--Awaler (talk) 09:57, 14 September 2011 (UTC)

I think the sentence is sensible; it's "obviously true" in the sense that it's (probabilistically) an a priori true statement about a finite set of numbers (whereas e.g. the twin prime conjecture is a statement about an infinite set of numbers). Roentgenium111 (talk) 16:03, 10 January 2018 (UTC)

$W_{16777213}$

Nearly, $W_{16777213}$ has been tested to be composite! So the conjecture is also true when p = 16777213. (See factorb)

67 and 257

Thr article states that 67 and 257 are composite, but they are, in fact, prime. Someone should change this. — Preceding unsigned comment added by 156.57.22.217 (talk) 18:41, 29 February 2016 (UTC)

Right, 67 and 257 are prime. What the article means is that 2^67-1 and 2^257-1 are composite, which is a true statement. Sorry for the misunderstanding.Rich (talk) 16:43, 3 October 2020 (UTC)