A163268 Primes p such that 1 + p + p^2 + p^3 + p^4 + p^5 + p^6 is prime.

2, 3, 5, 13, 17, 31, 61, 73, 89, 149, 163, 251, 349, 353, 461, 523, 599, 647, 863, 941, 947, 1087, 1117, 1229, 1277, 1291, 1297, 1409, 1439, 1489, 1567, 1579, 1609, 1627, 1753, 1783, 1831, 2039, 2131, 2293, 2531, 2609, 2753, 2861, 3037, 3163, 3167, 3299

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2009

Keywords

• nonn

Comments

Primes in A100330. The generated prime numbers are exactly A194257. [Bernard Schott, Dec 21 2012]

Links

• Robert Israel, Table of n, a(n) for n = 1..10000 (first 102 terms from Zak Seidov)

Crossrefs

Cf. A053182, A065509, A088550, A100330, A163268, A194257.

Programs

Maple

select(p -> isprime(p) and isprime(1+p+p^2+p^3+p^4+p^5+p^6), [2,seq(i,i=3..10000,2)]); # Robert Israel, May 05 2017

Mathematica

f[n_]:=1+n+n^2+n^3+n^4+n^5+n^6; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst,p]], {n,7!}]; lst
Select[Prime[Range[500]],PrimeQ[Total[#^Range[0,6]]]&] (* Harvey P. Dale, Jul 13 2022 *)

PARI

n=0;forprime(p=2,10000,isprime((p^7-1)/(p-1))&&print(n++" "p))\\ Zak Seidov, Mar 09 2013

Extensions

Edited (but not checked) by N. J. A. Sloane, Jul 25 2009