Primes in tuples II
By D. Goldston, Janos Pintz, C. Yalçin Yıldırım. 2007
80 citations recorded by the source corpus.
AbstractWe prove that $$ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $$where pn denotes the nth prime. Since on average pn+1−pn is asymptotically log n, this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p−p′ between primes which includes the small gap result above.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2a69b4a2c47bc52dc862c3d1aca0b14461b88e30
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Bounded gaps between primes (2014, background): “This is quite different from [6] and [7], in which various setsH are involved in the argument to derive results like (1.”