A014546 Primes in Sylvester's sequence A000058.

2, 3, 7, 43, 3263443

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

No more primes up to 21st recurrence step. - Artur Jasinski, Sep 20 2008

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.

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

Links

• Jens Kruse Andersen, Factorization of Sylvester's sequence
• Eric Weisstein's World of Mathematics, Sylvester's Sequence

Crossrefs

Cf. A000058, A091335.

Programs

Mathematica

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