
TL;DR
This paper demonstrates the existence of infinitely many pairs of consecutive primes with gaps larger than a specified function involving multiple iterated logarithms, advancing understanding of prime distribution.
Contribution
It introduces a novel approach combining recent sieve method progress with the Erdos-Rankin construction to establish large prime gaps, answering a longstanding question of Erdos.
Findings
Existence of large prime gaps exceeding a complex logarithmic function
Integration of modern sieve techniques with classical constructions
Progress towards understanding the distribution of prime gaps
Abstract
We show that there exists pairs of consecutive primes less than whose difference is larger than for any fixed . Our proof works by incorporating recent progress in sieve methods related to small gaps between primes into the Erdos-Rankin construction. This answers a well-known question of Erdos.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · History and Theory of Mathematics
