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 2022-07-05, 15:25 #1 charybdis     Apr 2020 100011101002 Posts Fields Medals 2022 ...have been awarded to Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska. No surprises here, unlike in 2018. Huh's award is further proof that the best way to win a Fields Medal in combinatorics is to connect it to other disciplines. Maynard is the one whose work will be most familiar to readers of this forum. He is most well-known for his proof that there are infinitely many pairs of primes separated by at most 600, but he has many other important and interesting results about prime numbers - for example he has proved that for every digit there are infinitely many primes that do not contain that digit.
 2022-07-18, 08:10 #2 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 7·173 Posts The bounded gaps between primes theorem can be seen here. https://asone.ai/polymath/index.php?...between_primes The best result is that there are an infinite number of pairs of primes that differ by at most 246. Maynard's result of 600 is good, but not the best so far. Have a nice day. Matt
2022-07-18, 10:44   #3
charybdis

Apr 2020

22×3×5×19 Posts

Quote:
 Originally Posted by MattcAnderson The best result is that there are an infinite number of pairs of primes that differ by at most 246. Maynard's result of 600 is good, but not the best so far. Have a nice day. Matt
Maynard's 600 was the best known bound at the time, and all the subsequent better bounds from Polymath were based on his work. His paper was also the first to show there are interval sizes that must contain 3, 4, 5... primes infinitely often.

 2023-06-02, 16:07 #4 pinhodecarlos     "Carlos Pinho" Oct 2011 Milton Keynes, UK 3·7·13·19 Posts https://youtu.be/qyctvtlIKu8 Public lecture by James Maynard.
 2023-06-02, 16:51 #5 firejuggler     "Vincent" Apr 2010 Over the rainbow 1011011010112 Posts I remembered a (then blog) page by Terrence tao on the subject from 2013. The math is beyond me. https://terrytao.wordpress.com/2013/...after-maynard/

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