Composite run around primes
Year: 2025
Type: preprint
Abstract: An explicit formula is provided to show that every positive even integer 2n can be written infinitely many ways as the difference of two odd integers with no primes in between. Two unbounded arithmetic progressions are identified in that formula, which are applied to prove that, for every 2n there exist infinitely many primes that are immediately followed by, or preceded by, a string of 2n-1 consecutive composite numbers. New insights into bounded gaps between primes of length $2< 2n\leq 246$ are introduced.
Author: Nunez, Hector Ivan
Institution: National Autonomous University of Honduras
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7104434390
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