

A075722


Numbers n such that 1 + n + n^s is a prime, s = 7.


3



1, 2, 15, 21, 29, 39, 42, 53, 57, 77, 81, 92, 117, 123, 131, 147, 149, 153, 167, 168, 200, 204, 207, 233, 249, 251, 252, 275, 278, 314, 317, 326, 357, 372, 378, 380, 410, 422, 434, 438, 440, 462, 467, 468, 498, 516, 546, 585, 587, 596, 608, 615, 621, 636
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


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=7 and find several first n's making n_s a prime (or a probable prime).


LINKS



EXAMPLE

15 is OK because at s=7, n=15, n_s = 1 + n + n^s = 170859391 is a prime.


MATHEMATICA



PROG

(Magma) [n: n in [0..1000]  IsPrime(s) where s is 1+n+n^7]; // Vincenzo Librandi, Jul 28 2014
(PARI) for(n=1, 10^3, if(isprime(n^7+n+1), print1(n, ", "))) \\ Derek Orr, Feb 07 2015


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



