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A128825
Primes p such that q = p+d (with d >= 6) is the next prime and both p and q are Sophie Germain primes.
7
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot, Apr 12 2007
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, Apr 15 2007
STATUS
approved