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
KEYWORD
nonn
AUTHOR
J. M. Bergot, Apr 12 2007
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, Apr 15 2007
STATUS
approved