Ibrahima Gueye, Twin Prime Numbers and Diophantine Equations, BSMaSS Volume 5, The Bulletin of Society for Mathematical Services and Standards (Volume 5) https://www.scipress.com/BSMaSS.5.10 Abstract: For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. Starting from Wilson's theorem, Clement’s theorem and the corollary of Clement’s theorem [1], I came to find Diophantine equations whose solution could lead to theproof of the infinitude of twin primes. Keywords: Clement’s Corollary, Clement’s Theorem, Diophantine Equations, Twin Primes, Wilson’s Theorem