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.

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

Author

Labos Elemer, Jan 29 2001

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005385, A005384, A058322, A059323, A059327.

Programs

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 *)