A075723 Numbers n such that 1 + n + n^6 is a prime.

1, 2, 3, 6, 8, 15, 17, 29, 30, 32, 45, 48, 59, 72, 74, 80, 87, 128, 141, 153, 155, 156, 158, 176, 182, 191, 197, 210, 216, 230, 273, 284, 293, 305, 314, 356, 366, 380, 384, 399, 402, 407, 408, 410, 413, 420, 435, 443, 447, 450, 473, 479, 497

Offset: 1

Author

Zak Seidov, Oct 03 2002

Keywords

• nonn
• easy

Comments

For s = 5,8,11,14,17,20,..., n_s=1+n+n^s is always composite for any n>1. Also at n=1, n_s=3 is a prime for any s. So it is interesting to consider only the cases of s != 5,8,11,14,17,20,... and n>1. Here I consider the case s=6 and find several first n's making n_s a prime (or a probable prime).

Examples

			15 is OK because at s=6, n=15, n_s = 1 + n + n^s = 11390641 is a prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002384, A049407, A049408.

Programs

Magma

[n: n in [0..500] | IsPrime(s) where s is 1+n+n^6]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[500], PrimeQ[1 + # + #^6] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

for(n=1,10^3,if(isprime(n^6+n+1),print1(n,", "))) \\ Derek Orr, Feb 07 2015