On the additive theory of prime numbers II

Details On the additive theory of prime numbers II On the additive theory of prime numbers II

2006-09-20

arxiv.org/abs/math/0609554v1

CSIT'2005 (Computer Science and Information Technologies, September 19-23, 2005, Yerevan, Armenia) (2005) 39-47

Mathematics

Logic

Scientific paper

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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