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A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.

%I A253941 #30 May 22 2025 10:21:42
%S A253941 184279409,619338131,913749803,1057351301,1507289869,1600204213,
%T A253941 2845213937,4725908767,4760956439,5374709801,5518707641,8724256757,
%U A253941 9044067313,9387396269,10992352517,11937043567,13493126359,13593105793,17891702891,17897035213,17954907767,19690938161,20227580927,20922685813,21313027583,21717176851
%N A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.
%C A253941 The sequence contains all terms up to 10^10. There are no terms as yet for which (p^12 + 5)/6 is also prime.
%C A253941 No terms < 10^11 with (p^12 + 5)/6 prime. - _Chai Wah Wu_, Jan 27 2015
%H A253941 Chai Wah Wu, <a href="/A253941/b253941.txt">Table of n, a(n) for n = 1..67</a>
%o A253941 (Python)
%o A253941 from gmpy2 import is_prime, t_divmod
%o A253941 A253941_list = []
%o A253941 for p in range(1,10**6,2):
%o A253941     if is_prime(p):
%o A253941         p2, x = p**2, 1
%o A253941         for i in range(5):
%o A253941             x *= p2
%o A253941             q, r = t_divmod(x+5,6)
%o A253941             if r or not is_prime(q):
%o A253941                 break
%o A253941         else:
%o A253941             A253941_list.append(p) # _Chai Wah Wu_, Jan 22 2015
%o A253941 (PARI) lista(nn) = forprime(p=5, nn, if(ispseudoprime((p^2 + 5)/6) && ispseudoprime((p^4 + 5)/6) && ispseudoprime((p^6 + 5)/6) && ispseudoprime((p^8 + 5)/6) && ispseudoprime((p^10 + 5)/6), print1(p, ", "))); \\ _Jinyuan Wang_, Mar 01 2020
%Y A253941 Subsequence of A253976.
%Y A253941 Cf. A118915, A247478, A253925, A253940.
%K A253941 nonn
%O A253941 1,1
%A A253941 _Zak Seidov_, Jan 20 2015
%E A253941 a(15)-a(26) from _Chai Wah Wu_, Jan 22 2015