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

Author

Zak Seidov, Jun 16 2015

Keywords

• nonn

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}.

Examples

			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)
		

Links

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

Crossrefs

Cf. A062718, A137270.

Programs

Magma

[p: p in PrimesUpTo(5000) | IsPrime(p^2-8)];  // K. D. Bajpai, Jun 18 2015

Mathematica

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

PARI

lista(nn) = forprime(p=2, nn, if (isprime(p^2-8), print1(p, ", "))); \\ Michel Marcus, Jun 16 2015