Infiniteness sets of primes, admitting diophantine representations in eight variables (Q1807459)
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scientific article; zbMATH DE number 1364694
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infiniteness sets of primes, admitting diophantine representations in eight variables |
scientific article; zbMATH DE number 1364694 |
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Infiniteness sets of primes, admitting diophantine representations in eight variables (English)
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22 November 1999
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The existence of infinite sets of primes which can be represented as the sets of positive values of some polynomials in a small number of variables is discussed (all variables range over positive integers). It is proved (nonreflexively) that there exists such a set, which has a representation with eight variables. This number of variables is smaller than in the best universal construction known today, which is ten. Also, some improvements of well-known technical lemmas are given.
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diophantine representation
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Hilbert's tenth problem
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prime numbers
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