On the additive theory of prime numbers II

Patrick Cegielski; Denis Richard; Maxim Vsemirnov

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On the additive theory of prime numbers II

Patrick Cegielski·Denis Richard·Maxim Vsemirnov

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Abstract

The undecidability of the additive theory of primes (with identity) as well as the theory Th(N,+, n -> p\_n), where p\_n denotes the (n+1)-th prime, are open questions. As a possible approach, we extend the latter theory by adding some extra function. In this direction we show the undecidability of the existential part of the theory Th(N, +, n -> p\_n, n -> r\_n), where r\_n is the remainder of p\_n divided by n in the euclidian division.

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BibTeX RIS

Patrick Cegielski, Denis Richard, Maxim Vsemirnov. 2006-09-20. On the additive theory of prime numbers II. https://arxiv.org/abs/math/0609554

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