A283191 Prime numbers p such that (2^p - 5)/3 is prime.

7, 13, 19, 31, 373, 811, 1117, 5059, 12601

Offset: 1

Author

Dmitry Ezhov, Mar 02 2017

Keywords

• nonn
• more

Comments

Let W = (2^p - 5)/3 and s = (W+1)/(2*p), then 5^s == 2 (mod W) for terms 1..9.

Subsequence of 7, 13, 19, 31, 51, 55, 85, 111, 319, 373,.. which are numbers m such that (2^m-5)/3 is prime. - R. J. Mathar, Mar 05 2017

a(10) > 3*10^5. - Michael S. Branicky, Jan 30 2025

Crossrefs

Cf. A000978.

Programs

Mathematica

Select[Prime@ Range[2, 1000], PrimeQ[(2^# - 5)/3] &] (* Michael De Vlieger, Mar 03 2017 *)

PARI

forprime(p=3, 30000, W= (2^p-5)/3; if(ispseudoprime(W), print1(p, ", ")))