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

1,1

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

R. Zumkeller, Table of n, a(n) for n = 1..49 (complete sequence)

Dario A. Alpern, Factorization using the Elliptic Curve Method [From Reinhard Zumkeller, May 14 2010]

Crossrefs

Cf. A001220, A172291-A172293, A177855, A046051, A046800.

Sequence in context: A050826 A086910 A101300 * A076524 A168279 A171957

Adjacent sequences: A172287 A172288 A172289 * A172291 A172292 A172293

Keyword

fini,full,nonn

Author

Artur Jasinski, Jan 30 2010

Extensions

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

Definition clarified corrected by Joerg Arndt, Apr 25 2011

Status

approved