A258572 Primes p such that p - 2, p^2 - 2, p^3 - 2, p^4 - 2 and p^5 - 2 are all prime.

15331, 3049201, 9260131, 10239529, 10955449, 24303469, 33491569, 42699721, 56341711, 66241561, 87068479, 114254629, 129783571, 143927419, 152065549, 221977909, 235529419, 252769399, 280028449, 284535481, 299116021, 312896359, 349665889, 361039519, 407462929

Offset

1,1

Comments

Intersection of A006512, A062326, A178251, A154832 and A154834.

Subsequence of primes of A216945. - Michel Marcus, Jul 07 2015

Links

Table of n, a(n) for n=1..25.

Mathematica

Select[Prime[Range[10^8]], And@@PrimeQ[{#, # - 2, #^2 - 2, #^3 - 2, #^4 - 2, #^5 - 2}] &] (* Vincenzo Librandi, Jul 06 2015 *)
Select[Prime[Range[2172*10^4]], AllTrue[#^Range[5]-2, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 02 2018 *)

Prog

(Magma) [p: p in PrimesUpTo(40000000) | IsPrime(p^1-2) and IsPrime(p^2-2) and IsPrime(p^3-2) and IsPrime(p^4-2) and IsPrime(p^5-2)];
(PARI) first(m)=my(v=vector(m), i, p, t=1); for(i=1, m, while(1, p=prime(t); if(isprime(p-2)&&isprime(p^2 - 2)&&isprime(p^3 - 2)&&isprime(p^4 - 2)&&isprime(p^5 - 2), v[i]=p; break, t++)); t++); v; /* Anders Hellström, Jul 17 2015 */

Crossrefs

Cf. A006512, A062326, A154832, A154834, A178251, A216945.

Sequence in context: A064982 A204317 A216945 * A352477 A232382 A175751

Adjacent sequences: A258569 A258570 A258571 * A258573 A258574 A258575

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 03 2015

Extensions

a(10) corrected and a(14)-a(25) added by Giovanni Resta, Jun 05 2015

Status

approved