10 conjectures in additive number theory

TL;DR

This paper proposes new conjectural methods for generating prime sequences using gcd-based algorithms and reformulates major additive number theory conjectures, supported by experimental results.

Contribution

It introduces a conjectural prime generation approach inspired by Rowland and offers new formulations of key additive number theory conjectures.

Findings

Primes generated often exceed expected bounds.

New formulations of classical conjectures.

Experimental evidence using pari-gp.

Abstract

Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much more greater than the number of required iterations. In an other hand we propose new formulations of famous conjectures from the additive theory of numbers (the weak twin prime conjecture, the Polignac conjecture, the Goldbach conjecture or the very general Schinzel's hypothesis H). For the moment these are experimental results obtained using pari-gp.