A059323 -id:A059323 - cp's OEIS frontend

A059394 Special safe primes (from A005385) such that the next prime is also a safe prime.

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

Labos Elemer, Jan 29 2001

nonn

			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).

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

Cf. A005385, A005384, A059322, A059323, A059327.

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

Labos Elemer, Jan 29 2001

nonn

			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.

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

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

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 *)

A274381 Safe primes p such that p + 24 is also a safe prime.

Original entry on oeis.org

23, 59, 83, 359, 479, 563, 839, 863, 1283, 2039, 2879, 2999, 3779, 4259, 4679, 5483, 7703, 10079, 12203, 13103, 23603, 26903, 27803, 30323, 31583, 33623, 35339, 41519, 43403, 44519, 44939, 53759, 55079, 57119, 57899, 58043, 65123, 66359, 70139, 70199, 76379, 77723, 79943

Offset: 1

Debapriyay Mukhopadhyay, Jun 23 2016

nonn

			83 is a safe prime and so is 83 + 24 = 107.
4679 is a safe prime and so is 4679 + 24 = 4703.

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A005385, A033560, A059323.

A274381:=n->`if`(type((n-1)/2, prime) and isprime(n+24) and isprime(n) and type((n+23)/2, prime), n, NULL): seq(A274381(n), n=1..10^5); # Wesley Ivan Hurt, Jun 25 2016

Select[Prime@ Range[10^4], PrimeQ[(# - 1)/2] && PrimeQ[# + 24] && PrimeQ[(23 + #)/2] &] (* Giovanni Resta, Jun 23 2016 *)
Select[Prime[Range[8000]],AllTrue[{(#-1)/2,(#+23)/2,#+24},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 31 2019 *)

lista(nn) = forprime(p=3, nn, if (isprime((p-1)/2) && isprime(q=p+24) && isprime((q-1)/2), print1(p, ", "))); \\ Michel Marcus, Jun 23 2016

{ x | both x and x + 24 are safe primes }.

cp's OEIS Frontend

A059394 Special safe primes (from A005385) such that the next prime is also a safe prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A274381 Safe primes p such that p + 24 is also a safe prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula