A297625 Primes of the form (2^(p^k) - 1)/(2^(p^(k - 1)) - 1), with p prime and k > 1.

5, 17, 73, 257, 65537, 262657, 4432676798593

Offset: 1

Author

Arkadiusz Wesolowski, Jan 04 2018

Keywords

• nonn

Comments

Primes of the form Phi(x, 2), where x is a proper prime power and Phi is the cyclotomic polynomial.

Together with 3, supersequence of A019434.

Also called Mersenne-Fermat primes.

a(8) has 1031 digits and is too large to include.

References

• Fredrick Kennard, Unsolved Problems in Mathematics, Lulu Press, 2015, p. 160.

Links

• Wikipedia, Mersenne-Fermat primes

Crossrefs

Cf. A019434, A051156, A140797, A187823, A245730, A246547.

Programs

Magma

lst:=[]; r:=7; pr:=PrimesUpTo(r); for k in [2..r] do for c in [1..#pr] do p:=pr[c]; if p^k le r^2 then MF:=Truncate((2^(p^k)-1)/(2^(p^(k-1))-1)); if IsPrime(MF) then Append(~lst, MF); end if; end if; end for; end for; Sort(lst);