TL;DR
This paper demonstrates new patterns in prime numbers that extend Green and Tao's result on arbitrarily long prime arithmetic progressions, revealing deeper structural properties of primes.
Contribution
It introduces generalized prime patterns that extend the Green-Tao theorem on arithmetic progressions in primes.
Findings
Existence of new prime patterns beyond arithmetic progressions
Generalization of Green-Tao theorem to broader prime configurations
Deeper understanding of prime distribution patterns
Abstract
In the present work the existence of some patterns of primes is shown which generalize the celebrated result of Green and Tao according to which there are arbitrarily long arithmetic progressions in the sequence of primes
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Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics · Advanced Mathematical Theories