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

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