2009/05/11 by Shaohua Zhang, Zhang, Shaohua · 1 citation
Mathematics · #11A41 #11A99 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.0905.1655
openalex publication_date 2009/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to try to establish a generic model for the problem that several multivariable number-theoretic functions represent simultaneously primes for infinitely many integral points. More concretely, we introduced briefly the research background-the history and current situation-from Euclid's second theorem to Green-Tao theorem. We analyzed some equivalent necessary conditions that irreducible univariable polynomials with integral coefficients represent infinitely many primes, found new necessary conditions which perhaps imply that there are only finitely many Fermat primes, obtained an analogy of the Chinese Remainder Theorem, generalized Euler's function, the prime-counting function and Schinzel-Sierpinski's Conjecture and so on. Nevertheless, this is only a beginning and it miles to go. We hope that number theorists consider further it.