Timeline for Primes that are "almost" multiples of each other

6 events

when toggle format	what		by	license	comment
Jul 21, 2017 at 21:19	comment	added	Sylvain JULIEN		Your question is in some sense dual to asking whether for some prime $ p $ , the set $ W_{p} : =\{k\in\mathbb{N}\colon\{kp-1,kp+1\}\cap P\neq\emptyset\} $, is infinite. For $ p =3$, a positive answer follows from the assumption of the twin prime conjecture.
Jul 21, 2017 at 6:08	vote	accept	Dominic van der Zypen
Jul 21, 2017 at 5:26	comment	added	Robert Israel		Yes, in fact for each prime $p$, Dirichlet's theorem says there are infinitely many primes of the form $kp-1$ and infinitely many of the form $kp+1$, so $\bigcup_{k \ge 2} M_k$ consists of all the primes.
Jul 21, 2017 at 5:23	answer	added	Robert Israel		timeline score: 12
Jul 21, 2017 at 4:16	comment	added	Dominic van der Zypen		I would assume one can prove that $\bigcup\{M_k:k\in\mathbb{N}, k\ge 2\}$ is infinite.
Jul 21, 2017 at 4:15	history	asked	Dominic van der Zypen	CC BY-SA 3.0