A348307 Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.

23, 21383, 26459, 28643, 111263, 137339, 217643, 333563, 342599, 423323, 486023, 540539, 548519, 567719, 658943, 671039, 755663, 829463, 865499, 890063, 903803, 976883, 1108259, 1168523, 1199183, 1308383, 1316699, 1318379, 1342403, 1349423, 1390199, 1501583, 1503059, 1558079, 1563119

Offset: 1

Author

Marc Morgenegg, Oct 11 2021

Keywords

• nonn

Comments

For (p-1)/2, those are the safe primes A005385.

Examples

			23 is a term because: (23-1)/2 = 11, (23-2)/3 = 7, 2*23+1 = 47, 3*23+2 = 71, {23, 11, 7, 47, 71} are all prime numbers.
		

Crossrefs

Cf. A005385 (safe primes).

Intersection of A005385 and A094524 and A005384 and A023208.

Programs

Mathematica

Select[Range[1, 1.5*10^6, 2], AllTrue[{#, (# - 1)/2, (# - 2)/3, 2*# + 1, 3*# + 2}, PrimeQ] &] (* Amiram Eldar, Oct 11 2021 *)

PARI

isok(p) = iferr(isprime(p) && isprime((p-1)/2) && isprime((p-2)/3) && isprime(2*p+1) && isprime(3*p+2), E, 0); \\ Michel Marcus, Oct 11 2021

Extensions

More terms from Michel Marcus, Oct 11 2021