Small Gaps Between Primes


Dan Goldston

San Jose State University


Thursday, November 16, 2006

Talk at 4:30 p.m. in Room 2-190

Tea from 4:00 - 4:30 p.m. in Room 2-290
Refreshments afterwards, in Room 2-290


Abstract:   I will talk about recent joint work with Janos Pintz and Cem Yildirim on small gaps between primes. A surprising consequence of our work is that if the primes are well distributed in arithmetic progressions then one can prove results not too far from the twin prime conjecture. For example, if the Elliott-Halberstam conjecture is true then there are infinitely many pairs of primes with difference 16 or less. Unconditionally we can prove a long-standing conjecture in the field: there are pairs of primes much closer together than the average distance between consecutive primes. This work has had its share of media attention, and even generated a song on public television. For me there has been three stages to this publicity: the fun of small-time public fame for proving the result with Yildirim three years ago, followed closely by the less fun publicity when Granville and Soundararajan showed how the proof crashed and burned beyond repair, and lastly the redemption following the strange emergence of a new proof. After Wiles this may seem like standard procedure in mathematics, but I would not recommend it for the faint of heart.


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Posted: October 16, 2006    URL: