A258992 Primes p such that p^2 - 8 is also prime.

5, 7, 11, 17, 19, 23, 31, 37, 53, 67, 101, 103, 149, 163, 173, 191, 227, 229, 241, 257, 269, 271, 313, 347, 353, 359, 367, 373, 383, 431, 467, 479, 487, 523, 541, 563, 577, 599, 613, 619, 647, 653, 661, 733, 761, 773, 823, 829, 859, 863, 919, 941, 1061, 1087

Offset

1,1

Comments

The first appearances of 2..6 consecutive primes in the sequence are: {31,37}, {5, 7, 11}, {353, 359, 367, 373}, {1293199, 1293203, 1293233, 1293239, 1293247}, {3982031, 3982037, 3982057, 3982067, 3982073, 3982079}.

Initial terms of the sets of exactly 6 consecutive primes: {3982031, 5495989, 33057589, 255414437, 495180067, 558985507}.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

From K. D. Bajpai, Jun 18 2015: (Start)
a(3) = 11: both 11 and 11^2 - 8 = 113 are prime.
a(4) = 17: both 17 and 17^2 - 8 = 281 are prime.
(End)

Mathematica

Select[Prime[Range[5000]], PrimeQ[#^2-8]&]  (* K. D. Bajpai, Jun 18 2015 *)

Prog

(PARI) lista(nn) = forprime(p=2, nn, if (isprime(p^2-8), print1(p, ", "))); \\ Michel Marcus, Jun 16 2015
(Magma)  [p: p in PrimesUpTo(5000) | IsPrime(p^2-8)];  // K. D. Bajpai, Jun 18 2015

Crossrefs

Cf. A062718, A137270.

Sequence in context: A073681 A364867 A155772 * A020582 A106863 A200569

Adjacent sequences: A258989 A258990 A258991 * A258993 A258994 A258995

Keyword

nonn

Author

Zak Seidov, Jun 16 2015

Status

approved