Number theory—probabilistic, heuristic, and computational approaches

Abstract

After the description of the models of Kubilius, Novoselov and Schwarz, and Spilker, respectively, a probability theory for finitely additive probability measures is developed by use of the Stone-Cech compactification of N . The new model is applied to the result of Erdős and Wintner about the limit distribution of additive functions and to the famous result of Szemerédi in combinatorial number theory. Further, it is explained how conjectures on prime values of irreducible polynomials are used in the search for large prime twins and Sophie Germain primes.