Bounded Gaps Between Primes

Speaker: Zihao (Travor) Liu
Location: Gordan St (25) Math 500
Abstract: In 2014, Yitang Zhang proved that there exists infinitely many pairs of consecutive primes with gap less than 7*10^7, an astonishing progress towards the twin prime conjecture. Few months later, this upper bound is sharpened to 600 by James Maynard, who received Fields medal in 2022 as a result of this achievement. Although Maynard's method is essentially independent from Zhang's, their works are built upon a sieve developed by Goldston, Pintz, and Yıldırım in 2009, whose ideas turn out be motivated by a 1947 research by Atle Selberg. In this colloquium, we will launch an ambitious adventure into the impressive works of these mathematicians. Pre-knowledge in analytic number theory is not required but would be helpful.

--------------------

--------------------

[adambui]

P<P there a-b=2, hence we prove the twin prime conjecture. Where is my 1M prize?

[johnnicholson]

The audio sucks. But, have you looked at Ramanujan primes? A corollary to Ramanujan primes proves a maximal gap G(m) is bounded by the prior maximal gap G(m-1). Namely, G(m) < 2 G(m-1).

[omargaber]

It's very ridiculous, I didn't understand any thing😢