20140528, 00:48  #34 
"Phil"
Sep 2002
Tracktown, U.S.A.
3×373 Posts 
Looks like 246, but the prospect for nearterm improvement is diminishing:
http://michaelnielsen.org/polymath1/...between_primes 
20140528, 20:05  #35  
Aug 2006
3·1,993 Posts 
Quote:
Zhang's original proof made no attempt to get a small bound, and 70 million was what he got by straightforward methods which lost a lot of efficiency. Later attempts reduced this by improving different parts of each of the steps. There are some ways of faking it. For example, assuming a hypothesis called EH is essentially pretending that we can get 100% efficiency on the first step. Last fiddled with by CRGreathouse on 20140528 at 20:06 

20141003, 00:15  #36  
"Gang aft agley"
Sep 2002
111010101010_{2} Posts 
The “bounded gaps between primes” Polymath project – a retrospective
30 September, 2014 http://terrytao.wordpress.com/2014/0...retrospective/ Quote:


20141114, 01:18  #37  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
sure that I heard him introduce "prime cousin" as a pair p and p+4', both prime and then (maybe) "sexy primes" for pair p and p+6, both prime. Then the Theorem  one of these three collectons p, p+2; p, p+4; and p, p+6 is infinite. He went one to say, probably all three are infinite, but that wasn't a theorem. That would include a proof that the gap is no more than 6. Maybe there was a conditional, that got left off of the interview? Nothing new on bounded gaps in Google. Someone else heard this? Bruce 

20141114, 02:18  #38  
Aug 2006
1011101011011_{2} Posts 
Quote:


20141114, 03:11  #39  
"Gang aft agley"
Sep 2002
2·1,877 Posts 
Quote:
Quote:


20141114, 11:51  #40  
Jun 2005
lehigh.edu
400_{16} Posts 
Quote:
reading about conditional gaps being 12 or perhaps 6.(and nothing possible below 6, by current methods) at that time. Guess this current formulation is just a restatement of what gap. of 6 means  one of those three sets necessarily infinite. Bruce 

20141114, 15:10  #41  
"Gang aft agley"
Sep 2002
2×1,877 Posts 
Quote:
Quote:


20141115, 06:27  #42 
Aug 2006
3·1,993 Posts 
Yes, that's stronger, but it still doesn't get you any more than "at least one of" {twin primes, cousin primes, sexy primes} being infinite. And actually all of the statements are of this sort, even the unconditional one.

20141117, 13:58  #43  
"Gang aft agley"
Sep 2002
2·1,877 Posts 
Quote:
Last fiddled with by only_human on 20141117 at 13:59 

20150101, 07:56  #44  
"Gang aft agley"
Sep 2002
2×1,877 Posts 
This one hour video by Terry Tao talks of the developments mentioned in this thread and elsewhere. Most helpfully for people trying to understand what this all means, he spends some time on sieve techniques.
Terry Tao, Ph.D. Small and Large Gaps Between the Primes (YouTube) Published on Oct 7, 2014, UCLA Department Of Mathematics On the large gap side he mentions a constant that is also mentioned in this blog entry: Long gaps between primes (16 December, 2014) for which he would reward progress: Quote:


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