%I #13 Sep 08 2022 08:45:30
%S 23,83,173,233,653,1013,1223,1499,1889,2063,2393,2543,2693,2963,3803,
%T 4373,5039,6101,6263,6323,6491,7079,7643,7883,9473,10691,13883,14153,
%U 14303,15161,16811,17669,19553,19913,20753,20759,21701,22259,22343
%N Primes p such that q = p+d (with d >= 6) is the next prime and both p and q are Sophie Germain primes.
%C Sophie Germain primes are primes p such that 2*p+1 is also prime.
%H Harvey P. Dale, <a href="/A128825/b128825.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%e 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.
%t 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 *)
%o (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
%Y Cf. A005384 (Sophie Germain primes).
%K nonn
%O 1,1
%A _J. M. Bergot_, Apr 12 2007
%E Edited, corrected and extended by _Klaus Brockhaus_, Apr 15 2007