A108573 Least positive k such that k * [RSA-640]^n - 1 is prime, where RSA-640 is the 193 decimal digit RSA challenge number A391940(14).

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

0,1

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

RSA-640 is A391940(14) = A391941(14)*A391942(14). - Antti Karttunen, Jan 01 2026

Links

Michael S. Branicky, Table of n, a(n) for n = 0..81

Wikipedia, RSA-640

Crossrefs

Cf. A108375, A108881, A391940, A391941, A391942.

Sequence in context: A193131 A193154 A120061 * A187942 A244670 A199146

Adjacent sequences: A108570 A108571 A108572 * A108574 A108575 A108576

Keyword

nonn,changed

Author

Jason Earls, Jul 05 2005

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

Status

approved