New progress in searching for Wieferich primes without a positive result. Wieferich@Home carries on the searching process!

For elMath.org: Miroslav Kures
Institute of Mathematics, Brno University of Technology
Contact: kures@fme.vutbr.cz
Creation date: 2009-02-16

Enter Page Title Here 1093 and 3511 are only two known Wieferich primes up to now. Knauer and Richstein searched for Wieferich primes up to 1.25x1015 with no other Wieferich primes. Their result was published in 2005. A few days ago, a new result was announced on http://www-personal.umich.edu/~dorais/docs/wieferich.pdf. Dorais and Klyve searched for Wieferich primes up to 6.7x1015 with no new discovery.

Certainly, Wieferich@Home ranges for searching for Wieferich primes are in unsearched area. Users can monitor this on http://www.elmath.org/index.php?id=statistics. Wieferich@Home project has also the periodic test testing independently very big numbers (up to 3500 bits) with periodic binary representation, see a conjecture on http://mathworld.wolfram.com/WieferichPrime.html. These numbers have a period i.e. binary digit string of the length of 24 bits at present.

We recall that everybody can participate in this project by running a free application on own computer (download on http://www.elmath.org/index.php?id=download); the solution can be important in number theory, maybe also in cryptography.

Author: Miroslav Kures