A014546 - OEIS

%I #29 Feb 16 2025 08:32:33

%S 2,3,7,43,3263443

%N Primes in Sylvester's sequence A000058.

%C No more primes up to 21st recurrence step. - _Artur Jasinski_, Sep 20 2008

%C Andersen's page shows that A000058(30) is the first number whose primality is unknown. Thus if a(6) exists it has over 218 million decimal digits.

%C Since 2019, according to Andersen's updated page, the first term with unknown status is A000058(32), showing that a(6), if it exists, has at least 874250789 digits. So it is safe to say it would be too huge to include. Andersen writes "According to heuristics based on the fast growth, it is unlikely that any s_i above s_5 is prime". Compare this to the possibility of a new Fermat prime A019434. - _Jeppe Stig Nielsen_, Jan 06 2025

%H Jens Kruse Andersen, <a href="http://primerecords.dk/sylvester-factors.htm">Factorization of Sylvester's sequence</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SylvestersSequence.html">Sylvester's Sequence</a>

%t a = {}; k = 2; Do[k = k^2 - k + 1; If[PrimeQ[k], AppendTo[a, k]], {n, 1, 15}]; a (* _Artur Jasinski_, Sep 20 2008 *)

%Y Cf. A000058, A091335.

%K nonn,changed

%O 1,1

%A _Eric W. Weisstein_