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A215057 Number of primes of the form 1 + b^64 for 1 < b < 10^n. 11


%S 0,0,8,92,606,4835,41059,354239,3133668

%N Number of primes of the form 1 + b^64 for 1 < b < 10^n.

%C Primes 1 + b^64 are a form of generalized Fermat primes.

%C It is conjectured that a(n) is asymptotic to 0.0616053*li(10^n)

%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">Status of the smallest base values yielding Generalized Fermat primes</a>

%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/stat.html">How many prime numbers appear in a sequence ?</a>

%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/ccdgfpn.html">A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)</a>

%e a(3) = 8 because the Fermat numbers F_6(b) where b<10^3 are prime only for b = 102, 162, 274, 300, 412, 562, 592, 728.

%o (PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^64+1))

%Y Cf. A215047, A215048, A215049, A215050, A215051, A215058.

%K nonn,more

%O 1,3

%A _Henryk Dabrowski_, Aug 01 2012

%E a(8)-a(9) from _Kellen Shenton_, Aug 09 2020

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Last modified August 5 17:08 EDT 2021. Contains 346488 sequences. (Running on oeis4.)