%0 Journal Article %T A Refinement of the Function $g(m)$ on Grimm Conjecture %A Shaohua Zhang %J Mathematics %D 2008 %I arXiv %X In this paper, we refine the function $g(x)$ on Grimm's conjecture and improve a result of Erd\"{o}s and Selfridge without using Hall's theorem. %U http://arxiv.org/abs/0811.0966v4