Goldbach Conjecture and the least prime number in an arithmetic progression

Shaohua Zhang

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arXiv · 0812.4610

Goldbach Conjecture and the least prime number in an arithmetic progression

Shaohua Zhang

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Abstract

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. Résumé La conjecture de Goldbach et le plus petit nombre premier dans une progression arithmétique Dans ce document, nous essayons d'étudier les relations entre la conjecture de Goldbach et le plus petit nombre premier dans une progression arithmétique. Nous donnons une nouvelle forme faible de la conjecture de Goldbach. Nous prouvons que cette forme affaiblie et une forme affaiblie de l'hypothèse de Chowla impliquent que tout entier pair suffisamment grand peut être écrit comme une somme de deux nombres premiers distincts.

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Shaohua Zhang. 2010-02-23. Goldbach Conjecture and the least prime number in an arithmetic progression. https://arxiv.org/abs/0812.4610

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