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A278869 Sophie Germain primes p such that p+6 and p-6 are primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A096342 A066179 A217566 * A272628 A141093 A041236

Adjacent sequences:  A278866 A278867 A278868 * A278870 A278871 A278872

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Nov 29 2016

STATUS

approved

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Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)