A215058 - OEIS

%I #17 Aug 11 2020 01:26:47

%S 0,0,7,25,242,1933,16080,139921,1234958

%N Number of primes of the form 1 + b^128 for 1 < b < 10^n.

%C Primes 1 + b^128 are a form of generalized Fermat primes.

%C It is conjectured that a(n) is asymptotic to 0.0242888*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) = 7 because the generalized Fermat numbers F_7(b) where b<10^3 are prime only for b: 120, 190, 234, 506, 532, 548, 960.

%o (PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^128+1))

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

%K nonn,more

%O 1,3

%A _Henryk Dabrowski_, Aug 01 2012

%E a(8)-a(9) from _Kellen Shenton_, Aug 10 2020