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arXiv · 1406.4996

Infinitely many pairs of primes $p$ and $p+2$

Guangchang Dong
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Abstract

We take the pre-sieved set to be all natural numbers $N=\{1,2,3,\dots\}$ with a sieve system:single sieve,double sieve,.... With single sieve, i.e. , remove out the multiple of a prime, we derive all the primes. With double sieve, i.e. , remove out the multiple and the multiple of a prime and $-2$ simultaneously, we get all the prime twins and prove that infinitely many prime twins exist under suitable conditions. Finally, with special 4 sieve, we prove that infinitely many prime twins exist without any restriction.

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Guangchang Dong. 2014-06-19. Infinitely many pairs of primes $p$ and $p+2$. https://arxiv.org/abs/1406.4996

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