A358381 Primes p such that q1=6*p-1 and q2=6*p+1 are also primes (twin primes) and q1 is a Sophie Germain prime (i.e., 2*q1+1 is prime).

2, 5, 7, 47, 107, 907, 2137, 2347, 3407, 4547, 4597, 8377, 9067, 9277, 9767, 14537, 16427, 18307, 19507, 19997, 23447, 23917, 26927, 27437, 28837, 29297, 33037, 37307, 38327, 45127, 46457, 50957, 52957, 55897, 59077, 59407, 60317, 63667, 65497, 69767, 74377, 77527, 86587, 86837

Offset: 1

Author

Tamas Nagy, Nov 12 2022

Keywords

• nonn

Comments

Except for the first 2 terms, every term's last digit is a 7 in base 10.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A060212.

Cf. A005384.

Programs

Maple

filter:= p -> andmap(isprime, [p, 6*p-1, 6*p+1, 12*p-1]):
select(filter, [2,5,seq(i,i=7..10^5,10)]); # Robert Israel, Dec 23 2022

Mathematica

Select[Prime[Range[8500]], PrimeQ[6*# - 1] && PrimeQ[6*# + 1] && PrimeQ[12*# - 1] &] (* Amiram Eldar, Nov 13 2022 *)