A059394
Special safe primes (from A005385) such that the next prime is also a safe prime.
Original entry on oeis.org
5, 7, 467, 1307, 2447, 5087, 5927, 12527, 18947, 44687, 55079, 78467, 79943, 83207, 93383, 103007, 105143, 111443, 118787, 128879, 143687, 164987, 196907, 204587, 207227, 208787, 229487, 232823, 236507, 257627, 267143, 275987, 289319, 296159
Offset: 1
For {467,55079,103007,728579,887759,..} safe primes {479,55103,103043,728627,887819} are the next primes, whose differences are 12,24,36,48,60,.. respectively,not necessarily equal to 12, the possible minimum (see A059322).
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ss[x_] := PrimeQ[(Prime[x]-1)/2]&&PrimeQ[(Prime[x+1]-1)/2] t=Prime[Flatten[Position[Table[ss[w], {w, 1, 100000}], True]]]
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.
Original entry on oeis.org
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
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.
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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 *)
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