# News summary

Search for Wieferich Primes through the Use of Periodic Binary Strings

Subject: Wieferich primes, Creation date: 2010-10-21, for elMath.org: Project Authors

The result of the distributed computing project Wieferich@Home is presented: the binary periodic numbers of bit pseudo-length j <= 3500 obtained by replication of a bit string of bit pseudo-length k <= 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.

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New progress in searching for Wieferich primes without a positive result. Wieferich@Home carries on the searching process! Subject: Wieferich primes, Creation date: 2009-02-16, for elMath.org: Miroslav Kures

1093 and 3511 are only two known Wieferich primes up to now. Knauer and Richstein searched for Wieferich primes up to 1.25x10

More information^{15}with no other Wieferich primes. Their result was published in 2005. Dorais and Klyve searched for Wieferich primes up to 6.7x10^{15}with no new discovery.

The 9th Central European Conference on Cryptography - Trebic'09 Creation date: 2009-01-08, for elMath.org: Project Authors

The conference CECC09 (June 23 -26, 2009) is the next in the series of Central European Conferences on Cryptography, a series which has become a traditional meeting of people interested in all areas of cryptography. The CECC series is organized every year since the year 2000 in one of the Central European countries - Austria, Czech Republic, Hungary, Slovak republic and Poland.

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One Year Public Launching Anniversary Creation date: 2008-12-29, for elMath.org: Project Authors

Project authors congratulate the best member

More informationEgon2008_G1 (Czech Republic)and congratulate the best teamAMD Users (International)on the first place in stats of Wieferich@Home.

Half Year Public Launching Anniversary Creation date: 2008-06-29, for elMath.org: Project Authors

Project authors congratulate the best member Egon2008_G1 (Czech Republic) and congratulate the best team AMD Users (International) on the first place in stats of Wieferich@Home.

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Wieferich@Home v.2.0 Creation date: 2008-02-04, for elMath.org: Jan Dobes

New version accelerates searching in complete and periodical test. Software makes use of totally new algorithms, which are very efficient for mathematical method: exponentiation and congruency. New units for complete test are 10x larger and in periodical test 1,5x larger.

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Near Wieferich primes Subject: Wieferich primes, Creation date: 2008-01-14, for elMath.org: Miroslav Kures

Let us express numbers (mod

More informationp^{2}) in a formZ+Apwith bothZ,Areduced (modp). Wieferich primes are defined by 2^{p}^{-1}≡ 1 (modp^{2}), i.e. 2^{p}^{-1}=1+0p. Thus, for Wieferich primes...

Wieferich primes and Mersenne primes Subject: Wieferich primes, Creation date: 2007-12-28, for elMath.org: Miroslav Kures

Let n ∈ N;

More informationMersenne numbersare defined by M_{n}=2^{n}−1. A binary expression of Mersenne numbers consists of units only. If M_{n}is a prime number, then n is a prime number. (The reverse implication need not hold.) ...

The abc conjecture and non-Wieferich primes Subject: Wieferich primes, Creation date: 2007-12-20, for elMath.org: Miroslav Kures

The known Wieferich primes are 1093 and 3511. It is not known, if there exist finitely or infinitely many Wieferich primes; Even it is not known, if there exist finitely or infinitely many non-Wieferich primes. However, we have a result allied to so-called abc-conjecture, which can be formulated for positive integers

More informationa,b,cas follows.

Find a third Wieferich prime Subject: Wieferich primes, Creation date: 2007-12-18, for elMath.org: Miroslav Kures

Arthur Wieferich was born on 27th April 1884 in MÃ¼nster, Germany. He had published five original papers, four of them (written in 1908 and 1909) turn out to be important for a development in the number theory. In the paper Zum letzten Fermat'schen Theorem, he demonstrates a relation between described primes and the most famous mathematical question (answered by Andrew Wiles, on June 23, 1993), Last Fermat Theorem.

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