A087490 Primes p such that 4^p - 3^p is composite.

5, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 293, 307

Offset: 1

Author

Cino Hilliard, Oct 26 2003

Keywords

• nonn

Comments

Primes not in A059801. - Robert Israel, Nov 03 2024

Links

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

Crossrefs

Cf. A005061, A059801.

Primes p such that k^p - (k-1)^p is composite: A087489 (k=3), this sequence (k=4), A087685 (k=5), A087749 (k=6), A087759 (k=7), A087763 (k=8), A087894 (k=9), A087895 (k=10).

Programs

Maple

filter:= p -> isprime(p) and not isprime(4^p-3^p):
select(filter, [seq(i,i=3..1000,2)]); # Robert Israel, Nov 03 2024

Mathematica

Select[Prime[Range[70]],CompositeQ[4^#-3^#]&] (* Harvey P. Dale, Mar 14 2025 *)

PARI

apmb(a,b,n) = { forprime(x=2,n, y=a^x-b^x; if(!ispseudoprime(y), print1(x","); ) ) }

Extensions

Offset corrected by Mohammed Yaseen, Jul 18 2022