Search for Wieferich Primes through the use of Periodic Binary Strings

The result of the distributed computing projectWieferich@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.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Разпределение на простите числа и някои приложения

Petar Popivanov - This talk deals with several classical and more modern results from the theory of primes and is devoted to a larger audience. A short survey is given and almost primes of order two are discussed too. Polynomials with integer coefficients are considered from the point of view of their composite and prime functional values. Exponential type functions mapping N into the set of primes are also constructed.