On The Infinity of the Set of Twin Primes
Abstract
If p and p - 2 are primes, they are called twin primes and p is called twin head. The main purpose of the paper is to prove that the set of twin primes is infinite.
References
K. H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1993.
P. Ribenboim, The Little Book of Bigger Primes, 2nd ed. New York: Springer-Verlag, 2004.
Y. Zhang, “Bounded gaps between primes,” Annals of Mathematics, vol. 179, no. 3, pp. 1121–1174, 2014.
J. Maynard, “Small gaps between primes,” Annals of Mathematics, vol. 181, no. 1, pp. 383–413, 2015.
D. H. J. Polymath, T. Tao, et al., “Variants of the Selberg sieve, and bounded intervals containing many primes,” Research in the Mathematical Sciences, vol. 1, no. 12, pp. 1–83, 2014.
T. Tao, “Open problems: The parity problem for sieve theory,” What’s New Blog, 2015. [Online]. Available: https://terrytao.wordpress.com/2015/04/07/open-problem-the-parity-problem-for-sieve-theory/
A. Granville, “Primes in intervals of bounded length,” Bulletin of the American Mathematical Society, vol. 52, no. 2, pp. 171–222, 2015.
E. Klarreich, “Prime number patterns finally found,” Quanta Magazine, 2013. [Online]. Available: https://www.quantamagazine.org/prime-number-patterns-finally-found-20130519/
K. Hartnett, “Mathematicians prove the existence of infinitely many prime number pairs in function fields,” Quanta Magazine, 2019. [Online]. Available: https://www.quantamagazine.org/mathematicians-prove-twin-prime-conjecture-in-function-fields-20190410/
