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