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: Creation date: 2009-02-16

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://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://elmath.org/index.php?id=download); the solution can be important in number theory, maybe also in cryptography.

Author: Miroslav Kures

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Subjects

• Search for Wieferich Primes through the Use of Periodic Binary Strings
• New progress in searching for Wieferich primes without a positive result. Wieferich@Home carries on the searching process!
• Near Wieferich primes