%I A050920 #37 Jun 30 2026 05:18:53
%S A050920 3,393050634124102232869567034555427371542904833
%N A050920 Cullen primes: primes of the form n*2^n+1.
%C A050920 The next term is too large to display here, having 1423 digits. See A005849.
%D A050920 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.
%H A050920 Ray Ballinger, <a href="http://www.prothsearch.com/cullen.html">Cullen Primes: Definition and Status</a>.
%H A050920 Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=6">Cullen Primes</a>.
%H A050920 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CullenNumber.html">Cullen Number</a>.
%F A050920 a(n) = A002064(A005849(n)).
%e A050920 1 * 2^1 + 1 = 3, which is prime.
%e A050920 141 * 2^141 + 1 = 393050634124102232869567034555427371542904833, which is also prime.
%e A050920 The third Cullen prime is approximately 2.677114856136697933736444 * 10^1422.
%t A050920 Select[Table[n * 2^n + 1, {n, 5000}], PrimeQ] (* _Harvey P. Dale_, Dec 14 2014 *)
%Y A050920 See A005849 for the corresponding n.
%Y A050920 Cf. A002064.
%K A050920 nonn,nice,bref
%O A050920 1,1
%A A050920 _N. J. A. Sloane_, Dec 30 1999