A270972 Primes p such that p-2, p^2-2 and p^3-2 are all prime.

19, 8629, 9721, 12109, 13831, 15331, 17029, 17989, 25849, 33151, 56209, 70999, 73039, 78541, 92461, 97369, 97609, 103069, 103969, 147139, 174469, 179719, 203341, 217369, 221401, 242059, 249541, 269431, 277549, 283009, 285559, 324619, 333451, 346669, 393079, 404269, 409261, 424891, 440551, 488689

Offset: 1

Author

Emre APARI, Mar 27 2016

Keywords

• nonn

Comments

Subsequence of A006512. - Altug Alkan, Mar 27 2016

Examples

			p=19; p-2 = 17 (is prime), p^2-2 = 359 (is prime), p^3-2 = 6857 (is prime).
		

Crossrefs

Cf. A000040, A001248, A006512, A030078, A049001, A040976, A153481.

Programs

Magma

[p: p in PrimesUpTo(500000) | IsPrime(p-2) and IsPrime(p^2-2) and IsPrime(p^3-2)]; // Vincenzo Librandi, Mar 28 2016

Mathematica

Select[Prime@ Range@ 42000, Function[k, AllTrue[k^# & /@ Range@ 3 - 2, PrimeQ]]] (* Michael De Vlieger, Mar 27 2016, Version 10 *)

PARI

lista(nn) = {forprime(p=5, nn, if(isprime(p-2) && isprime(p^2-2) && isprime(p^3-2), print1(p, ", ")));} \\ Altug Alkan, Mar 27 2016

Extensions

More terms from Altug Alkan, Mar 27 2016