TL;DR
This paper proves the existence of infinitely many prime pairs with gaps no greater than 84 by constructing a new sieve weight and support, leveraging the Bombieri-Vinogradov theorem.
Contribution
It introduces a novel sieve weight and support that enable the application of the Bombieri-Vinogradov theorem to bound prime gaps.
Findings
Infinitely many prime pairs with gap ≤ 84 proven
New sieve weight and support constructed
Application of Bombieri-Vinogradov theorem to prime gaps
Abstract
It is proven that there are infinitely prime pairs whose difference is no greater than 84. In proving that result, a new sieve weight is constructed. The new idea is to construct the largest sieve support which admits the use of the Bombieri-Vinogradov theorem.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Mathematical Identities