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Links I found interesting for 15-06-2013

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( 3 comments — Leave a comment )
makyo
Jun. 15th, 2013 08:16 am (UTC)
First proof that infinitely many prime numbers come in pairs
Zhang did the difficult general work to show that the range was finite, and gave a construction for an upper bound of 70 million. Since then, a bunch of other mathematicians have used his methods to find more optimal bounds, and according to this, by a couple of weeks ago it was down to about 4 million.
nwhyte
Jun. 15th, 2013 09:02 am (UTC)
Hooray! Maybe we can get it down to 2!
gareth_rees
Jun. 15th, 2013 11:15 am (UTC)
The world's number theorists (well, mostly Andrew Sutherland) are working hard on it, and if everything on that page checks out, the gap was down to 248,898 as of 14th June. (This kind of parameter optimization will most likely peter out well before the gap is in single digits, and then there will need to be more conceptual breakthroughs.)

Update: down to 12,006 as of 1st July.

Edited at 2013-07-01 08:18 am (UTC)
( 3 comments — Leave a comment )

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