On the additive theory of prime numbers II

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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Patrick Cegielski, Denis Richard, Maxim Vsemirnov. On the additive theory of prime numbers II. 2005, pp.39-47. ⟨hal-00096769⟩

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