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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 1.25x1015 with no other Wieferich primes. Their result was published in 2005. Dorais and Klyve searched for Wieferich primes up to 6.7x1015 with no new discovery.

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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 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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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 p2) in a form Z+Ap with both Z, A reduced (mod p). Wieferich primes are defined by 2p-1 ≡ 1 (mod p2), i.e. 2p-1=1+0p. Thus, for Wieferich primes...

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Wieferich primes and Mersenne primes

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

Let n ∈ N; Mersenne numbers are defined by Mn=2n−1. A binary expression of Mersenne numbers consists of units only. If Mn is a prime number, then n is a prime number. (The reverse implication need not hold.) ...

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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 a,b,c as follows.

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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 Münster, 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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