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Old 2022-04-05, 09:33   #78
MJansen
 
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Default Updated wiki page

Now the verification by Andreas is complete, I edited the wikipedia page on prime gaps:
https://en.wikipedia.org/wiki/Prime_...erical_results

Kind regards
Michiel
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Old 2022-04-09, 20:58   #79
Bobby Jacobs
 
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Thanks! It is always great to update Wikipedia.
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Old 2022-04-10, 13:02   #80
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Great result. I'm stepping away from processing large number of gaps, as I will be in another country for 2 years and wont have the resources.

I will keep plugging away with one gap, which is currently 11th largest, where I haven't found either end point. I have high hopes!
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Old 2022-04-10, 17:17   #81
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Quote:
Originally Posted by robert44444uk View Post
Great result. I'm stepping away from processing large number of gaps, as I will be in another country for 2 years and wont have the resources.

I will keep plugging away with one gap, which is currently 11th largest, where I haven't found either end point. I have high hopes!
Sounds interesting Robert! What country if I may ask?
PS my last search is currently 5th and close to 4th with both endpoints still to be found. High hopes here as well ;-)

Kind regards
Michiel
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Old 2022-04-11, 16:02   #82
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https://primegap-list-project.github...-gaps-by-size/

Why is it (and many of the other top gaps) listed as ??? instead of PRP? Both endpoints are both Lucas PRPs and SPRPs to many bases.
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Old 2022-04-11, 16:51   #83
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I believe this happens when the server (AKA: my computer) doesn't fully verify the gap.

There's some discussion in Prime Gap News (see #126 and Prime Gap Records (see #48 through #52)
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Old 2022-04-12, 19:03   #84
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Quote:
Originally Posted by SethTro View Post
I believe this happens when the server (AKA: my computer) doesn't fully verify the gap.

There's some discussion in Prime Gap News (see #126 and Prime Gap Records (see #48 through #52)
Hi Seth,

This is what Thomas wrote at his site:
The classifications of the gaps are shown in positions 10-14. Position 10 is an asterisk for maximal gaps, otherwise a blank. Position 11 is always blank. Position 12 is (in this table) always a "C", indicating an ordinary or common prime gap. Position 13 is ordinarily a "?", indicating that the gap is a first known occurrence, but that it is not known whether or not it is a true first occurrence. This character would be an "F" if the gap had been proven a first occurrence, or an "N" if it had been proven not a first occurrence. Position 14 is a "P" if the bounding primes are probabilistic, or a "C" if the bounding primes have been certified deterministically.
If position 14 is a "?" (classification code "C??"), the bounding integers are probable primes (primes or strong base-2 pseudoprimes), but the interior integers of the gap have not been verified all composite to the satisfaction of Thomas R. Nicely; consequently, there remains a significant possibility that such a gap may in fact be smaller in measure than indicated, due to the as yet undetected presence of an interior prime.



Since Andreas verified the largest gap, in Thomas's definition this gap should have a stronger qualification like C?V, all other gaps in the top 20 (https://primegap-list-project.github...-gaps-by-size/) only should have C?P as far as I know.

So how to go from the qualificiation as used by Thomas to a new one?
You could add C?P in front of the number of digits instead of PRP/???

And C?V for the largest gap since that gap has been verified.

So
1 6966714 ???208096 = 479909#/30030-3166622 14.5395 Jansen and Jens Kruse Andersen 2022
2 6582144 PRP216841 = 499973#/30030 - 4509212 13.1829 Martin Raab 2017
3 6480930 ???208093 = 479909#/9699690-2492758 13.5259 Jansen and Jens Kruse Andersen 2022
4 6181674 ???208094 = 1*479909#/510510-3758926 12.9012 Jansen and Jens Kruse Andersen 2022
5 5198448 ???157490 = 363257*363269#/510510-2177806 14.3353 Jansen and Jens Kruse Andersen 2021
6 5103138 PRP216849 = 281*499979#/46410 - 2702372 10.2203 Robert W. Smith 2016


Would become
1 6966714 C?V208096 = 479909#/30030-3166622 14.5395 Jansen and Jens Kruse Andersen 2022
2 6582144 C?P216841 = 499973#/30030 - 4509212 13.1829 Martin Raab 2017
3 6480930 C?P208093 = 479909#/9699690-2492758 13.5259 Jansen and Jens Kruse Andersen 2022
4 6181674 C?P208094 = 1*479909#/510510-3758926 12.9012 Jansen and Jens Kruse Andersen 2022
5 5198448 C?P157490 = 363257*363269#/510510-2177806 14.3353 Jansen and Jens Kruse Andersen 2021
6 5103138 C?P216849 = 281*499979#/46410 - 2702372 10.2203 Robert W. Smith 2016

PS if you change the list lay-out could you change gap 6181674 to 479909#/510510-3758926 (instead of 1*479909#/510510-3758926)?

Kind regards
Michiel
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Old 2022-04-13, 06:30   #85
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Quote:
Originally Posted by MJansen View Post
Hi Seth,

Since Andreas verified the largest gap, in Thomas's definition this gap should have a stronger qualification like C?V, all other gaps in the top 20 (https://primegap-list-project.github...-gaps-by-size/) only should have C?P as far as I know.

So how to go from the qualificiation as used by Thomas to a new one?
You could add C?P in front of the number of digits instead of PRP/???

And C?V for the largest gap since that gap has been verified.

Kind regards
Michiel
I committed some old code I had worked on verify (using ecpp-dj and sage's ecpp) the endpoints of small gaps.
This is a dual verification that it's easy to run on the small gaps.

I don't have a ton of energy to update the primegap-list-project.github.io site. I suspect some of the _layout files could/should be moved to a macro.

For the larger gaps I dislike manually editing the sql file, but I suspect it's the reasonable path forward. For completion sake can you link the posts where each of these (6966714, 6480930, 6181674, 5198448) was verified? I'll then included a link to that post in the commit message.
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Old 2022-04-13, 09:33   #86
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Quote:
Originally Posted by SethTro View Post
For the larger gaps I dislike manually editing the sql file, but I suspect it's the reasonable path forward. For completion sake can you link the posts where each of these (6966714, 6480930, 6181674, 5198448) was verified? I'll then included a link to that post in the commit message.
6966714: In this thread post #76 and #66
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Old 2022-04-14, 21:51   #87
MJansen
 
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Default New absolute gap record

As of tonight a new absolute gap record is in the making. Primorial 29*479909#/9699690 has surpassed 6966714 and no gap ends are found yet. Keep you informed as it progresses.

Kind regards
Michiel
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Old 2022-04-16, 00:01   #88
MJansen
 
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Default New absolute gap record

Alas, both end points have been found rather quickly:

The gap of primorial 29*479909#/9699690 is 7186572, with 208095 digits and merit 14.998450.
The gap has end points:
29*479909#/9699690-3531714
and
29*479909#/9699690+3654858

After pre-sieving with all primes till 10^12 and PRP-ing the remaining candidates between 10 January 2022 and 16 April 2022 00:58 (real) local time, the gap was found. Standardized to one core at 3500 MHz, pre-sieving took 84 hours and it took 6027 hours and 37 minutes to PRP 36.375 remaining candidates.

Again I wished it had turned out a bit bigger, but it is a new record (for now) and that is enough. I will quit the search for large gaps for now.

Kind regards
Michiel Jansen

Last fiddled with by MJansen on 2022-04-16 at 00:06 Reason: added number of digits
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