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### "Prime Numbers: It has been a Good Millennium So Far"

**Special Events**

Speaker: | Daniel Goldston, San Jose State |

Related Webpage: | https://en.wikipedia.org/wiki/Daniel_Goldston |

Location: | 1147 MSB |

Start time: | Fri, Oct 26 2018, 1:45PM |

No mathematicians from the distant past of 1999 would have predicted the progress that has now been made in our knowledge of primes, although they might be even more shocked about other changes in the world of 2018. The Green-Tao theorem from 2004 showed there are infinitely often arbitrarily long arithmetic progressions of primes, instead of progression of 3 primes known before. The current record for a numerically known such progression has 26 primes. The Odd Goldbach Conjecture that every odd number greater than 5 is the sum of three primes was proved in 2013 by Helfgott; this was only known in 2002 to be true for all odd numbers larger than 10^1346. And thanks to Zhang and Maynard-Tao building on work of Goldston-Pintz-Yildirim, we know there are infinitely often primes a bounded distance apart - bounded is 246 at the moment. Unlike the first two results, proving bounded gaps between primes isn't that difficult to teach in a beginning graduate class because it isn't nearly as hard a problem as we thought. On the other hand, the twin prime conjecture may be really hard.

There will be a reception with light refreshments from 3:45-4:15 in the lobby of the Mathematical Sciences Building.