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.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 5)

Pages:

10-13

DOI:

10.18052/www.scipress.com/BSMaSS.5.10

Citation:

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:

Mar 2013

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

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.