A289363 Primes p such that p^2 + p - 1 is composite.

7, 17, 23, 29, 37, 43, 47, 61, 67, 71, 73, 79, 97, 107, 109, 113, 127, 137, 139, 151, 157, 167, 173, 179, 197, 211, 223, 227, 229, 239, 251, 257, 269, 271, 277, 283, 293, 307, 311, 313, 317, 337, 347, 353, 359, 367, 379, 383, 389, 397, 409, 421, 439, 443, 457, 467, 479, 487, 491, 503, 509, 521, 523

Offset: 1

Author

Robert Israel, Jul 04 2017

Keywords

• nonn

Comments

Includes all primes == 2 (mod 5) or == 3 or 7 (mod 11) except 2 and 3.

If p is in this sequence, p^2 + p is not in A241884 although p^2 + p - 1 is composite.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A241884.

Programs

Magma

[p: p in PrimesUpTo(600) | not IsPrime(p^2+p-1)]; // Vincenzo Librandi, Jul 05 2017

Maple

select(t -> isprime(t) and not isprime(t^2+t-1), [seq(i,i=1..1000, 2)]);

Mathematica

Select[Prime[Range[100]], CompositeQ[#^2+#-1]&] (* Jean-François Alcover, Jul 18 2017 *)

PARI

lista(nn) = forprime(p=2, nn, if (!isprime(p^2+p-1), print1(p, ", "))); \\ Michel Marcus, Jul 05 2017