A253976 - OEIS

A253976

Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6 and (p^8 + 5)/6 are prime.

%I #15 Jul 23 2023 01:54:14

%S 67103,7524593,9938069,10125793,13042637,55741139,55792241,58429099,

%T 77618323,92713879,94554613,96242761,103774049,119753549,141725501,

%U 142915193,164899799,165227399,173202247,174728233,178411771,184279409,184356703,186622003,195863347,200406977,239488649

%N Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6 and (p^8 + 5)/6 are prime.

%H Zak Seidov, <a href="/A253976/b253976.txt">Table of n, a(n) for n = 1..503</a> (all terms up to 10^10)

%t Select[Prime[Range[132*10^5]],AllTrue[(#^Range[2,8,2]+5)/6,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 11 2018 *)

%o (PARI) forprime(p=1,10^7,k=0;for(i=1,4,P=(p^(2*i)+5)/6;if(P\1==P,if(ispseudoprime(P),k++);if(!ispseudoprime(P),k=0;break));if(P\1!=P,k=0;break));if(k,print1(p,", "))) \\ _Derek Orr_, Jan 21 2015

%Y Subsequence of A253939. Cf. A118915, A247478, A253939, A253940, A253941.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 21 2015