A172290 Prime divisors of 2^1092-1, listed with multiplicities.

3, 3, 5, 7, 7, 13, 13, 29, 43, 53, 79, 113, 127, 157, 313, 337, 547, 911, 1093, 1093, 1249, 1429, 1613, 2731, 3121, 4733, 5419, 8191, 14449, 21841, 121369, 224771, 503413, 1210483, 1948129, 22366891, 108749551, 112901153, 23140471537, 25829691707, 105310750819, 467811806281, 4093204977277417, 8861085190774909, 556338525912325157, 86977595801949844993, 275700717951546566946854497, 292653113147157205779127526827, 3194753987813988499397428643895659569

Offset: 1

Author

Artur Jasinski, Jan 30 2010

Keywords

• fini
• full
• nonn

Comments

Up to now only two primes p such that p^2 divide 2^(p-1)-1 are known (these two are Wieferich primes, see A001220).

The sequence is finite with A001222(2^1092-1) = 49 terms; A001221(2^1092-1) = 45. - Reinhard Zumkeller, May 14 2010

Terms appearing more than once (in fact twice) are 3, 7, 13, and 1093.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..49 (complete sequence)
• Dario A. Alpern, Factorization using the Elliptic Curve Method.

Crossrefs

Cf. A001220, A172291, A177855, A046051, A046800, A242715.

Extensions

Missing terms a(34) and a(35) inserted by Reinhard Zumkeller, May 14 2010

Definition clarified and terms corrected by Joerg Arndt, Apr 25 2011