A108375 -id:A108375 - cp's OEIS frontend

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

Jason Earls, Jul 05 2005

nonn

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

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

Cf. A108375.

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

A108881 Least positive k such that k * [RSA-2048]^n + 1 is prime, where RSA-2048 is the 617 decimal digit RSA challenge number.

Original entry on oeis.org

290, 2430, 5012, 4680, 794, 2574, 26000, 3948, 18056, 10974

Offset: 1

Jason Earls, Jul 14 2005

Another term is a(16)=6766. All values in the sequence are Fermat and Lucas PRPs except for the first which was proved with ECM. The larger values won't be easily provable until RSA-2048 is factored, which has a prize of $200000 for its factorization.

Wikipedia, RSA-2048

Cf. A108375, A108573.

cp's OEIS Frontend

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

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