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A297625
Primes of the form (2^(p^k) - 1)/(2^(p^(k - 1)) - 1), with p prime and k > 1.
0
5, 17, 73, 257, 65537, 262657, 4432676798593
OFFSET
1,1
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.
PROG
(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);
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved