A215698 - OEIS

%I #5 Aug 22 2012 21:06:15

%S 0,0,4,30,272,2322

%N Number of primes of the form 1 + b^256 for 1 < b < 10^n.

%C Primes 1 + b^256 are a form of generalized Fermat primes.

%C It is conjectured that a(n) is asymptotic to 0.0290422*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) = 4 because the generalized Fermat numbers F_8(b) where b<10^3 are prime only for b: 278, 614, 892, 898.

%o (PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^256+1))

%Y Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058.

%K nonn

%O 1,3

%A _Henryk Dabrowski_, Aug 21 2012