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A059395
Smaller of safe prime twins: special safe primes (A005385) p such that the next prime is also the next safe prime and is p+12, i.e., occurs at the closest possible distance, 12.
1
467, 1307, 2447, 5087, 5927, 12527, 18947, 44687, 78467, 83207, 118787, 143687, 164987, 196907, 204587, 207227, 208787, 229487, 236507, 257627, 275987, 297707, 330887, 339827, 367007, 369647, 394007, 454907, 458807, 474347, 534827, 536087
OFFSET
1,1
LINKS
EXAMPLE
The pairs (5,7) and (7,11) are omitted, albeit are both consecutive primes and consecutive safe primes, however their distances (2 and 4) are singular. Cases [467, 439] and [20738027, 20738039] are pairs are both consecutive of consecutive primes and consecutive safe primes in minimal distance=12. The corresponding twins of Sophie Germain primes are [233, 239] or [1369013, 1369019] in distance 6.
MATHEMATICA
safeQ[p_] := PrimeQ[(p-1)/2]; seq={}; c=0; p1 = p2 = 11; q1 = safeQ[p1]; While[c < 30, p2 = NextPrime[p2]; q2 = safeQ[p2]; If[q1 && q2 && p2 == p1 + 12, c++; AppendTo[seq, p1]]; p1 = p2; q1 = q2]; seq (* Amiram Eldar, Jan 13 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 29 2001
STATUS
approved