TL;DR
This paper reviews recent progress on weak forms of the Prime $k$-tuple Conjecture, highlighting their implications for understanding small and large gaps between primes.
Contribution
It synthesizes recent advances and explores their impact on prime gap estimates, advancing the understanding of prime distribution.
Findings
Improved estimates for small prime gaps
New bounds for large prime gaps
Enhanced understanding of prime $k$-tuple Conjecture
Abstract
We discuss recent advances on weak forms of the Prime -tuple Conjecture, and its role in proving new estimates for the existence of small gaps between primes and the existence of large gaps between primes.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Limits and Structures in Graph Theory