A108573 Least positive k such that k * [RSA-640]^n - 1 is prime, where RSA-640 is the 193 decimal digit RSA challenge number.

3, 390, 1334, 136, 2058, 2710, 2082, 748, 2388, 3588, 1902, 988, 9170, 5076, 28778, 2112, 1800, 3082, 1238, 12916, 5090, 22312, 8412, 11068, 2, 1558, 67710, 3018, 22554, 1212, 3692, 29940, 204, 31432, 15392, 2922, 4524, 11418, 12638, 5500, 12158, 4626, 15384, 5718

Offset: 0

Author

Jason Earls, Jul 05 2005

Keywords

• nonn

Comments

Other terms are a(25)=1558 and a(43)=5718. All values in the sequence are Fermat and Lucas PRPs except for the first two which were proved with ECM. The larger values won't be easily provable until RSA-640 is factored, which has a prize of $20,000 for its factorization. This sequence is based on a suggestion of Jens Kruse Andersen.

RSA-640 was factored in 2005; see the Wikipedia link. - D. S. McNeil, Nov 26 2010

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..81
• Wikipedia, RSA-640

Crossrefs

Cf. A108375.

Extensions

Edited and a(19) added by D. S. McNeil, Nov 25 2010

a(0) prepended and a(20) and beyond from Michael S. Branicky, May 16 2025