A128825 Primes p such that q = p+d (with d >= 6) is the next prime and both p and q are Sophie Germain primes.

23, 83, 173, 233, 653, 1013, 1223, 1499, 1889, 2063, 2393, 2543, 2693, 2963, 3803, 4373, 5039, 6101, 6263, 6323, 6491, 7079, 7643, 7883, 9473, 10691, 13883, 14153, 14303, 15161, 16811, 17669, 19553, 19913, 20753, 20759, 21701, 22259, 22343

Offset

1,1

Comments

Sophie Germain primes are primes p such that 2*p+1 is also prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

653 and 659 are consecutive primes with difference 6. 2*653 + 1 = 1307 is prime and 2*659 + 1 = 1319 is prime. Hence 653 is a term.
1499 and 1511 are consecutive primes with difference 12 >= 6. 2*1499 + 1 = 2999 is prime and 2*1511 + 1 = 3023 is prime. Hence 1499 is a term.

Mathematica

Select[Partition[Prime[Range[3000]], 2, 1], #[[2]]-#[[1]]>5 && AllTrue[ 2#+1, PrimeQ]&][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 21 2018 *)

Prog

(Magma) [ p : p in PrimesUpTo(25000) | d ge 6 and IsPrime(2*p+1) and IsPrime(2*(p+d)+1) where d is NextPrime(p)-p ]; // Klaus Brockhaus, Apr 15 2007

Crossrefs

Cf. A005384 (Sophie Germain primes).

Sequence in context: A052073 A213174 A256376 * A339475 A167573 A318356

Adjacent sequences: A128822 A128823 A128824 * A128826 A128827 A128828

Keyword

nonn

Author

J. M. Bergot, Apr 12 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 15 2007

Status

approved