  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.
