本文通过Ｌ函数非零区域的扩张及相应的素数分布均值问题的研究证明了：每一个奇数Ｎ≥ｅｘｐ（ｅｘｐ（９．７１５））都能够表示成为三个素数之和．

By the investigation of the zero-free region of Dirichlet L-functions and the meanvalue estimate of the distribution of primes, we proved in this paper that every odd integer N ≥ exp(exp(9.715)) can be written as a sum of three primes.