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This result implies the existence of an infinitely repeatable prime 2-tuple, [2] thus establishing a theorem akin to the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013, [6] his first publication since his last paper in 2001. [18] The proof was refereed by leading experts in analytic number theory. [7]
A stronger form of the twin prime conjecture, the Hardy–Littlewood conjecture (see below), postulates a distribution law for twin primes akin to the prime number theorem. On 17 April 2013, Yitang Zhang announced a proof that there exists an integer N that is less than 70 million, where there are infinitely many pairs of primes that differ by ...
The main topic of the book is the conjecture that there exist infinitely many twin primes, dating back at least to Alphonse de Polignac (who conjectured more generally in 1849 that every even number appears infinitely often as the difference between two primes), and the significant progress made recently by Yitang Zhang and others on this problem.
The Twin Prime Conjecture. ... That was cleverly proven in 2013 by Yitang Zhang at the University of New Hampshire. ... mathematicians have been improving that number in Zhang’s proof, from ...
In other words: There are infinitely many cases of two consecutive prime numbers with difference n. [2] Although the conjecture has not yet been proven or disproven for any given value of n, in 2013 an important breakthrough was made by Yitang Zhang who proved that there are infinitely many prime gaps of size n for some value of n < 70,000,000.
In 2013 Yitang Zhang showed [17] that there are infinitely many prime pairs with gap bounded by 70 million, and this result has been improved to gaps of length 246 by a collaborative effort of the Polymath Project. [18]
For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal. [7]In November 2013, Maynard gave a different proof of Yitang Zhang's theorem [8] that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any there are infinitely many intervals of bounded length containing prime numbers. [9]
Yitang Zhang: bounded gap conjecture: number theory: The sequence of gaps between consecutive prime numbers has a finite lim inf. See Polymath Project#Polymath8 for quantitative results. 2013: Adam Marcus, Daniel Spielman and Nikhil Srivastava: Kadison–Singer problem: functional analysis