Timeline for How many primes have the form $(2^p+1)/3$?

6 events

when toggle format	what		by	license	comment
May 29, 2015 at 1:41	comment	added	Jeremy Rouse		Observe that if $(2^{p}+1)/3 = q^{a}$ for some prime $q > 2$ and $a \geq 2$, then the $2^{2p} \equiv 1 \pmod{q^{a}}$ so the order of $2$ modulo $q^{a}$ is a divisor of $2p$, and also a divisor of $(q-1) q^{a-1}$, by Euler's theorem. Since $\gcd(p,q) = 1$, this implies that $2^{q-1} \equiv 1 \pmod{q^{a}}$, and so $q$ is a Wieferich prime.
May 29, 2015 at 0:09	answer	added	Robert Israel		timeline score: 8
May 28, 2015 at 23:54	vote	accept	Huangjun Zhu
May 28, 2015 at 23:20	answer	added	Max Alekseyev		timeline score: 7
May 28, 2015 at 23:18	answer	added	Gerry Myerson		timeline score: 11
May 28, 2015 at 22:57	history	asked	Huangjun Zhu	CC BY-SA 3.0