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Twin Prime Numbers and Diophantine Equations

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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.


The Bulletin of Society for Mathematical Services and Standards (Volume 5)
I. Gueye, "Twin Prime Numbers and Diophantine Equations", The Bulletin of Society for Mathematical Services and Standards, Vol. 5, pp. 10-13, 2013
Online since:
March 2013

Ibrahima GUEYE, A note on the twin primes, South Asian Journal of Mathematics, Volume 2 (2012) Issue 2, pp.159-161.

PA Clement, Congruences for sets of premiums, American Mathematical Monthly 56 (1949), pp.23-25.

Viggo Brun, Series 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + .. where denominators are twin primes, is convergent or over, Bulletin of Mathematical Sciences 43 (1919), pp.100-104 and 124-128.

http: /fr. wikipedia. org/wiki/Nombres_premiers_jumeaux.

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