The problem of the least prime number in an arithmetic progression and its applications to Goldbach's conjecture

2009/12/01 by Shaohua Zhang, Zhang, Shaohua
Mathematics · #11A41 #11A99 #11B25 #11P32 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #General Mathematics (math.GM) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.0912.0147

openalex publication_date 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The problem of the least prime number in an arithmetic progression is one of the most important topics in Number Theory. In [11], we are the first to study the relations between this problem and Goldbach's conjecture. In this paper, we further consider its applications to Goldbach's conjecture and refine the result in [11]. Moreover, we also try to generalize the problem of the least prime number in an arithmetic progression and give an analogy of Goldbach's conjecture.

Citations

• Euclid's Number-Theoretical Work
• Primes in arithmetic progressions to large moduli

Related

• Goldbach Conjecture and the least prime number in an arithmetic progression
• Dealing with prime numbers I.: On the Goldbach conjecture
• The Least Prime in Arithmetic an Progression
• Definitive Proof of Goldbach's conjecture
• Goldbach's problem with primes in arithmetic progressions and in short intervals