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List of Misconceptions and Prime Gap Checkin


Wikipedia, List of common misconceptions, here. via Big Picture

George Washington did not have wooden teeth. His dentures were made of gold, hippopotamus ivory, lead, and human and animal teeth (including horse and donkey teeth).[32

Christian Perfect, The Aperiodical, Bound on prime gaps decreasing by leaps and bounds, here. This feels a little bit like Shelby Lyman broadcasting Fischer Spassky. I like it. Fischer still has google name search pole position.

The bound quickly tumbled much further than that, and Terry Tao initiated a new Polymath project to coordinate efforts. Participants are trying to optimise three constants:

  • H is a quantity such that there are infinitely many pairs of consecutive primes of distance at most H apart. Would like to be as small as possible.
  • k0 is a quantity such that every admissible k0-tuple has infinitely many translates which each contain at least two primes. Would like to be as small as possible.
  • ϖ is a technical parameter related to a specialized form of the Elliott-Halberstam conjecture. Would like to be as large as possible. Improvements in ϖ lead to improvements in k0.

Records are being kept on the Polymath wiki, and progress is swift: just yesterday eighteen different values for H were recorded, along with four values of k0. As I write, they currently think that H≤108,540. Of course, in the rough and tumble of mathematicians trading arguments through comments pages it’s entirely possible that mistakes will go unnoticed, but it’s certainly fun to watch!

Interested followers should take a look at an online reading seminar conducted by Terry Tao which is going through the original paper.


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