On the difference between consecutive primes

By James Maynard. 2012

266 citations recorded by the source corpus.

Update: This work reproduces an earlier result of Peck, which the author was initially unaware of. The method of the proof is essentially the same as the original work of Peck. There are no new results. We show that the sum of squares of differences between consecutive primes $\sum_{p_n\le x}(p_{n+1}-p_n)^2$ is bounded by $x^{5/4+{\epsilon}}$ for $x$ sufficiently large and any fixed ${\epsilon}>0$. The proof relies on utilising various mean-value estimates for Dirichlet polynomials.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/0f8a05d0a901fd261bcd5d35caa865333bc1ff00

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Moore Graphs and Beyond: A survey of the Degree/Diameter Problem (2013, methodology): “In order to obtain a lower bound for the remaining values of ∆, we may use the following fact [162] about the distribution of prime numbers: For an arbitrary ε > 0, there is a constant bε such that for any natural m there is a prime between m and bεm .”
PRIME POLYNOMIALS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS (2013, background): “Heath-Brown [6], improving Huxley [8], proves Conjecture 1.1, unconditionally, for x 7 12 −ǫ(x) ≤ Φ(x) ≤ x log4 x , where ǫ(x) → 0.”
Large gaps between consecutive prime numbers (2014, background): “525 and due to Baker, Harman and Pintz [1].”