A273871 Primes p such that (4^(p-1)-1) == 0 mod ((p-1)^2+1).

3, 5, 17, 257, 8209, 59141, 65537, 649801

Offset: 1

Author

Jaroslav Krizek, Jun 01 2016

Keywords

• nonn
• more

Comments

Prime terms from A273870.

The first 5 known Fermat primes from A019434 are in this sequence.

Conjecture 1: also primes p such that ((4^k)^(p-1)-1) == 0 mod ((p-1)^2+1) for all k >= 0.

Conjecture 2: supersequence of Fermat primes (A019434).

Examples

			5 is a term because (4^(5-1)-1) == 0 mod ((5-1)^2+1); 255 == 0 mod 17.
		

Crossrefs

Cf. A019434, A273870.

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and (4^(n-1)-1) mod ((n-1)^2+1) eq 0];

PARI

is(n)=isprime(n) && Mod(4,(n-1)^2+1)^(n-1)==1 \\ Charles R Greathouse IV, Jun 08 2016