On Wilson's Theorem and Polignac Conjecture
  We introduce Wilson's theorem and Clement's result and present a necessary and sufficient condition for p and p+2k to be primes where k is a positive integer. By using Simiov's Theorem, we derive an improved version of Clement's result and characterizations of Polignac twin primes which parallel previous characterizations. 
Lin Cong, and Zhipeng Li (Hwa Chong Junior College)