Goldbach Conjecture and the least prime number in an arithmetic progression

Details Goldbach Conjecture and the least prime number in an arithmetic progression Goldbach Conjecture and the least prime number in an arithmetic progression

2008-12-25

arxiv.org/abs/0812.4610v7

Mathematics

General Mathematics

This is the final version. In press as: S. Zhang, Goldbach Conjecture and the least prime number in an arithmetic progression,

Scientific paper

In this Note, we try to study the relations between the Goldbach Conjecture and the least prime number in an arithmetic progression. We give a new weakened form of the Goldbach Conjecture. We prove that this weakened form and a weakened form of the Chowla Hypothesis imply that every sufficiently large even integer may be written as the sum of two distinct primes. R\'{e}sum\'{e} La conjecture de Goldbach et le plus petit nombre premier dans une progression arithm\'{e}tique Dans ce document, nous essayons d'\'{e}tudier les relations entre la conjecture de Goldbach et le plus petit nombre premier dans une progression arithm\'{e}tique. Nous donnons une nouvelle forme faible de la conjecture de Goldbach. Nous prouvons que cette forme affaiblie et une forme affaiblie de l'hypoth\`{e}se de Chowla impliquent que tout entier pair suffisamment grand peut \^{e}tre \'{e}crit comme une somme de deux nombres premiers distincts.

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