Ibrahima Gueye, Twin Prime Numbers and Diophantine Equations, BSMaSS Volume 5, The Bulletin of Society for Mathematical Services and Standards (Volume 5)
    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.
    Clement’s Corollary, Clement’s Theorem, Diophantine Equations, Twin Primes, Wilson’s Theorem