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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A005384, A006489.

Sequence in context: A066179 A217566 A347141 * A272628 A141093 A041236

Adjacent sequences: A278866 A278867 A278868 * A278870 A278871 A278872

Keyword

nonn

Author

K. D. Bajpai, Nov 29 2016

Status

approved