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Large gaps between primes. Pages 915-933 from Volume 183 (2016), Issue 3 by James Maynard. Abstract. We show that there ...

We give an exposition of the 2018 paper "Long Gaps Between Primes" by Ford, Green, Konyagin, Maynard, and Tao. Using methods from analytic number theory, sieve theory, and hypergraph covering, the authors proved a new lower bound on the large gaps between consecutive primes, improving a previous one made some 80 years ago. Physics 119

Download Citation | Large gaps between primes | We show that there exists pairs of consecutive primes less than $x$ whose difference is larger.

Aug 31, 2014 · Large gaps between primes By James Maynard Abstract We show that there exist 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 a;) (log log log x) ~2 for any fixed t. This answers a well-known question of Erdös. 1. Introduction

Let X be a large number, and consider the least prime gap pn+1 − pn with pn,pn+1 ∈ [X,2X]. The prime number theorem tells us that there are. (1 + o(1)) X log ...

James Maynard on discoveries about large gaps between prime numbers.More links & stuff in full description below ↓↓↓More Maynard videos: ...

as the average gap between the prime numbers which are ⩽ X is ∼ log X. In ... of consecutive large gaps between primes, by combining the methods in this ...

Theorem: There are arbitrarily large gaps between consecutive primes. (In other words, it is possible to find arbitrarily large sets of consecutive non‐prime numbers.)

We give an exposition of the 2018 paper "Long Gaps Between Primes" by Ford, Green, Konyagin, Maynard, and Tao. Using methods from analytic number theory, sieve theory, and hypergraph covering, the authors proved a new lower bound on the large gaps between consecutive primes, improving a previous one made some 80 years ago. Physics 119

Warning: there are two standard definitions of "gap". Let p be a prime and q be the next prime. Some define the gap between these two primes to be the number of composites between them, so g = q - p - 1 (and the gap following the prime 2 has length 0). Others define it to be simply q - p (so the gap following the prime 2 has the length 1).

Our proof works by incorporating recent progress in sieve methods related to small gaps between primes into the Erdos-Rankin construction.

31.08.2014 · Large gaps between primes By James Maynard Abstract We show that there exist 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 a;) (log log log x) ~2 for any fixed t. This answers a well-known question of Erdös. 1. Introduction

James Maynard on discoveries about large gaps between prime numbers.More links & stuff in full description below ↓↓↓More Maynard videos: http://bit.ly/JamesM...

Large gaps between primes | Annals of Mathematics Large gaps between primes Pages 915-933 from Volume 183 (2016), Issue 3 by James Maynard Abstract We show that there exist 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.

Therefore, the difference between two successive primes p_k and p_(k+1) bounding a ... is the length of the largest prime gap that begins with a prime p_k ...

If p is a prime, the 'prime gap' after p is the number of composites that follow it. maximal gaps are larger than those for any smaller primes p.

Theorem: There are arbitrarily large gaps between consecutive primes. (In other words, it is possible to find arbitrarily large sets of consecutive non‐prime numbers.)

Large gaps between primes | Annals of Mathematics Large gaps between primes Pages 915-933 from Volume 183 (2016), Issue 3 by James Maynard Abstract We show that there exist 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.