A278869 Sophie Germain primes p such that p+6 and p-6 are primes.

11, 23, 53, 173, 233, 593, 653, 1103, 1223, 2693, 2903, 2963, 4793, 5303, 6263, 6323, 7823, 9473, 10253, 11783, 12653, 13463, 15803, 20753, 25673, 27743, 27773, 29873, 31253, 33623, 38183, 38453, 39233, 40283, 41603, 44273, 44543, 54443, 54773, 59393, 60083, 62213

Offset: 1

Author

K. D. Bajpai, Nov 29 2016

Keywords

• nonn

Comments

Intersection of A005384 and A006489.

After a(1), all the terms are congruent to 3 mod 10.

A prime p is Sophie Germain prime if 2*p+1 is also prime.

Examples

			11 is in the list because: 2*11 + 1 = 23 (prime), hence 11 is Sophie Germain prime; also, 11 - 6 = 5 and 11 + 6 = 17 are both prime.
23 is in the list because: 2*23 + 1 = 47 (prime), hence 23 is Sophie Germain prime; also, 23 - 6 = 17 and 23 + 6 = 29 are both prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..9180

Crossrefs

Cf. A000040, A005384, A006489.

Programs

Mathematica

Select[Prime[Range[20000]], PrimeQ[2 # + 1] && PrimeQ[# + 6] && PrimeQ[# - 6] &]

PARI

forprime(p=1,10000, if(isprime(2*p+1) && isprime(p+6) && isprime(p-6), print1(p, ", ")))