Mathematics – General Mathematics
Scientific paper
2009-05-11
Mathematics
General Mathematics
Added recent results, see [101-103]. This paper is dedicated to my great mother Caiying Cao, born on January 12, 1943--died on
Scientific paper
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.
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