# Unheralded Mathematician Bridges the Prime Gap



## Jcgrey

by: Erica Klarreich

On April 17, a paper arrived in the inbox of Annals of Mathematics, one of the discipline's preeminent journals. Written by a mathematician virtually unknown to the experts in his field - a 50-something lecturer at the University of New Hampshire named Yitang Zhang - the paper claimed to have taken a huge step forward in understanding one of mathematics' oldest problems, the twin primes conjecture.

Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic's current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track.

Just three weeks later - a blink of an eye compared to the usual pace of mathematics journals - Zhang received the referee report on his paper.

"The main results are of the first rank," one of the referees wrote. The author had proved "a landmark theorem in the distribution of prime numbers."

Rumors swept through the mathematics community that a great advance had been made by a researcher no one seemed to know - someone whose talents had been so overlooked after he earned his doctorate in 1992 that he had found it difficult to get an academic job, working for several years as an accountant and even in a Subway sandwich shop.

more

http://simonsfoundation.org/features/science-news/unheralded-mathematician-bridges-the-prime-gap/


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## Arthur Pendragon

Mathematics is one of those fields where anyone can strike gold, if given the right thought at the right time. Usually strokes of genius occur when you are younger, but this man has _miraculously _discovered a great improvement in prime number theory. I just hope that the _friend _that he visited to achieve this epiphany receives his due credit.


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## Arthur Pendragon

> Zhang's idea was to use not the GPY sieve but a modified version of it, in which the sieve filters not by every number, but only by numbers that have no large prime factors.


Recently, _k_0 has not been prime, although that was not always the case (earlier this year). Given that _k_0 has to be less than or equal to _H_, and _H_ must be 2, at some point given the rough relationship _H = k_0log_k_0 + _k_0, they must find a better solution for _k_0 as it would need to cease being an integer, unless _k_0 _= _1, which would be ridiculous.

Therefore, even if this route is optimized, a considerable fundamental breakthrough is still required to lower the limit below 10.


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## Sacrieur

My intuition tells me it's simpler than all of this.

It has to work that way.


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## Mersault

Very good 

I stopped reading it due to the Riemannian connection (which is still based on a hypothesis as far as i know, even for the parts of it used here?), but i am very happy such progress has been made. (i am not being pompous, btw, i just like math and observe it as a non-mathematician)


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