Sudden Progress on Prime Number Problem Has Mathematicians Buzzing

Erica Klarreich in Wired:

ScreenHunter_413 Nov. 23 16.25On May 13, an obscure mathematician — one whose talents had gone so unrecognized that he had worked at a Subway restaurant to make ends meet — garnered worldwide attention and accolades from the mathematics community for settling a long-standing open question about prime numbers, those numbers divisible by only one and themselves. Yitang Zhang, a lecturer at the University of New Hampshire, showed that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes separated by at most 70 million. His finding was the first time anyone had managed to put a finite bound on the gaps between prime numbers, representing a major leap toward proving the centuries-old twin primes conjecture, which posits that there are infinitely many pairs of primes separated by only two (such as 11 and 13).

In the months that followed, Zhang found himself caught up in a whirlwind of activity and excitement: He has lectured on his work at many of the nation’s preeminent universities, has received offers of jobs from top institutions in China and Taiwan and a visiting position at the Institute for Advanced Study in Princeton, N.J., and has been told that he will be promoted to full professor at the University of New Hampshire.

Meanwhile, Zhang’s work raised a question: Why 70 million? There is nothing magical about that number — it served Zhang’s purposes and simplified his proof. Other mathematicians quickly realized that it should be possible to push this separation bound quite a bit lower, although not all the way down to two.

More here.