20180418, 15:25  #1 
Jun 2003
Suva, Fiji
2^{3}×3×5×17 Posts 
The Next Prime Gap Project
I've been doing a bit of thinking around what this group might do when we reach 2^64.
One idea would be to extend Dr Nicely's list of prime gaps between 100000 and 200000. There is at least one gap known for all possible gaps between 0 and 108674 (and all are of merit greater than 10 except 85934) but there are many gaps lengths where there is no known pair of consecutive primes. Some statistics: Code:
From To No candidates % 100000 109998 1 0.02% 110000 119998 12 0.24% 120000 129998 73 1.46% 130000 139998 297 5.94% 140000 149998 815 16.30% 150000 159998 1488 29.76% 160000 169998 2126 42.52% 170000 179998 2816 56.32% 180000 189998 3333 66.66% 190000 199998 3757 75.14% ……………. ……………. 14718 29.44% 
20180420, 07:50  #2 
Jun 2003
Suva, Fiji
2^{3}·3·5·17 Posts 
I've started my own personal search in the region. After 3 days, on my spanking new 16 core computer, I have found 41 of the missing gaps including 117968 as well as two gaps over 200k, 253926 and 204004. The larger of these has a merit of 25.14.
danaj keeps a dynamic page which shows the smallest gaps for which no candidate is known: http://ntheory.org/gaps/stats.pl 
20180420, 12:49  #3 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
13FA_{16} Posts 
Have you tried your new machine on gap12?

20180420, 17:20  #4 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
1110001101_{2} Posts 
Looks like I have 970 gaps ready to submit  I need to do that soon. A few merit 34s and 33s. No gaps over 100k.

20180423, 08:22  #5 
Jun 2003
Suva, Fiji
3770_{8} Posts 

20180430, 08:31  #6 
Jun 2003
Suva, Fiji
2^{3}×3×5×17 Posts 
I just posted my first two weeks of results (615 records) to Dr Nicely, this included first time gaps, the smallest of which were as follows:
Code:
112186 117968 124114 124904 126842 127196 Code:
255486 24.19 253926 25.15 213780 27.31 Last fiddled with by robert44444uk on 20180430 at 08:35 
20180512, 20:40  #7 
May 2018
5^{2}×11 Posts 
We could try to find gaps between primes above 2^64.

20180514, 14:46  #8 
Jun 2003
Suva, Fiji
2^{3}·3·5·17 Posts 
I just submitted my latest 588 records gaps. This included 31 first time gaps in the 100k to 200k range and 3 larger than 200k. The smallest new gap was 125882, and there were no others smaller than 130k.
Good merit gaps were found for Code:
201198 24.78 205608 23.10 208216 25.14 
20180601, 09:06  #9 
Jun 2003
Suva, Fiji
2^{3}×3×5×17 Posts 
Another 2 weeks,. and another set of results  this time 323 results, of which 76 were first time gaps. The smallest of these was 125912, but also 126154
I'm in the zone now where first time gaps should be more common  searching around factorial 10687 where the smallest gap with no candidate is just about 10 merit. Other notable gaps this time: 248304 23.49 213880 20.89 206724 21.08 206616 20.87 201864 21.70 And at the other end of the scale: 2850 27.93 I'm also searching for very large gaps, I have one at the moment where the gap will be a minimum of 2834646 
20180601, 22:08  #10 
May 2018
5^{2}×11 Posts 
That is cool!

20180602, 17:49  #11 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
2×2,557 Posts 
Can I request if we can concentrate our CPU resources in finalising the search up to 2^64, lets finish what we have started a year ago please. Can we do that? Come on?

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