Bounded Gaps Between Prime Numbers: Individual Research Versus Crowd-Sourcing

Monday, 16 February 2015: 9:45 AM-11:15 AM
Room LL21C (San Jose Convention Center)
Studied since antiquity, our knowledge of prime numbers recently took a giant leap forward. This leap was accomplished both by the old-school method of an individual quietly working out intricate details and the decidedly new-school paradigm of crowdsourcing. What was not known before had been famously conjectured for centuries: infinitely often, there are two primes a bounded distance away from each other. A proof was announced in 2013 by the relatively unknown mathematician Yitang Zhang. It was quickly realized that his proof was correct, and then the fun began on the internet as many people chipped away at Zhang's initial bound of 7 x 107. Along the way, new techniques were discovered that placed the result in a wider context and further reduced the bound. Now, the bound is down to 246. So should mathematics progress with single researchers plugging away, as did Zhang (and before him, Wiles in his celebrated proof of Fermat's last theorem)? Or is crowdsourcing really the wave of the future?
Carl Pomerance, Dartmouth College
Daniel A. Goldston, San Jose State University
Yitang Zhang, University of New Hampshire
Bounded Gaps Between Primes, Finally!
Paul P. Pollack, University of Georgia
Big Doings from Small Gaps
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