# Large gaps between primes

@article{Maynard2014LargeGB,
title={Large gaps between primes},
author={James Maynard},
journal={arXiv: Number Theory},
year={2014}
}
• J. Maynard
• Published 1 August 2014
• Mathematics
• arXiv: Number Theory
We show that there exists pairs of consecutive primes less than $x$ whose difference is larger than $t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}$ for any fixed $t$. 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.
Large gaps between consecutive prime numbers
• Mathematics
• 2014
Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdos, we show that $$G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log Long gaps between primes • Mathematics, Computer Science • 2014 The main new ingredient is a generalization of a hypergraph covering theorem of Pippenger and Spencer, proven using the R\"odl nibble method. Large gaps between consecutive prime numbers containing perfect powers • Mathematics • 2015 For any positive integer k, we show that infinitely often, perfect kth powers appear inside very long gaps between consecutive prime numbers, that is, gaps of size$$\displaystyle{c_{k}\frac{\log
Bounded gaps between primes in short intervals
• Mathematics
• 2017
Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $$[x-x^{0.525},x]$$[x-x0.525,x] for large x. In this paper, we extend a result of Maynard
On the gaps between consecutive primes
• Mathematics, Computer Science
• 2018
The result concerning the least primes in arithmetic progressions concerning then-th prime is obtained and a related result about the small primes is obtained.
Note On The Maximal Primes Gaps
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In the present work we prove a common generalization of Maynard–Tao’s recent result about consecutive bounded gaps between primes and of the Erdős–Rankin bound about large gaps between consecutive
Limit points and long gaps between primes
• Mathematics
• 2015
Let $d_n = p_{n+1} - p_n$, where $p_n$ denotes the $n$th smallest prime, and let $R(T) = \log T \log_2 T\log_4 T/(\log_3 T)^2$ (the "Erd{\H o}s--Rankin" function). We consider the sequence
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Erd\"os conjectured that the set J of limit points of d_n/logn contains all nonnegative numbers, where d_n denotes the nth primegap. The author proved a year ago (arXiv: 1305.6289) that J contains an

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Large gaps between consecutive prime numbers
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• 2014
Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdos, we show that G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log
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Abstract LetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results of Erdős, Rankin, Schonhage, and Maier-Pomerance, we prove G(X)⩾(2e γ +o(1)) log Xlog 2 Xlog 4
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Consider a system ψ of nonconstant affine-linear forms ψ 1 , ... , ψ t : ℤ d → ℤ, no two of which are linearly dependent. Let N be a large integer, and let K ⊆ [-N, N] d be convex. A generalisation