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Old 2018-04-18, 15:25   #1
robert44444uk
 
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Default 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%
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Old 2018-04-20, 07:50   #2
robert44444uk
 
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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
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Old 2018-04-20, 12:49   #3
pinhodecarlos
 
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"Carlos Pinho"
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Have you tried your new machine on gap12?
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Old 2018-04-20, 17:20   #4
danaj
 
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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.
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Old 2018-04-23, 08:22   #5
robert44444uk
 
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Quote:
Originally Posted by pinhodecarlos View Post
Have you tried your new machine on gap12?
I should, once I get the chance, it would be interesting to see how it sings.
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Old 2018-04-30, 08:31   #6
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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
Large gaps with large merits include:
Code:
255486 24.19
253926 25.15
213780 27.31

Last fiddled with by robert44444uk on 2018-04-30 at 08:35
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Old 2018-05-12, 20:40   #7
Bobby Jacobs
 
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We could try to find gaps between primes above 2^64.
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Old 2018-05-14, 14:46   #8
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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
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Old 2018-06-01, 09:06   #9
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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
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Old 2018-06-01, 22:08   #10
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That is cool!
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Old 2018-06-02, 17:49   #11
pinhodecarlos
 
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"Carlos Pinho"
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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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