20220405, 09:33  #78 
Jan 2018
110_{10} Posts 
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 
20220409, 20:58  #79 
May 2018
10F_{16} Posts 
Thanks! It is always great to update Wikipedia.

20220410, 13:02  #80 
Jun 2003
Suva, Fiji
7F8_{16} Posts 
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! 
20220410, 17:17  #81  
Jan 2018
156_{8} Posts 
Quote:
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 

20220411, 16:02  #82 
Einyen
Dec 2003
Denmark
3·1,129 Posts 
https://primegaplistproject.github...gapsbysize/
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. 
20220411, 16:51  #83 
"Seth"
Apr 2019
19×23 Posts 
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) 
20220412, 19:03  #84  
Jan 2018
6E_{16} Posts 
Quote:
This is what Thomas wrote at his site: The classifications of the gaps are shown in positions 1014. 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 base2 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://primegaplistproject.github...gapsbysize/) 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#/300303166622 14.5395 Jansen and Jens Kruse Andersen 2022 2 6582144 PRP216841 = 499973#/30030  4509212 13.1829 Martin Raab 2017 3 6480930 ???208093 = 479909#/96996902492758 13.5259 Jansen and Jens Kruse Andersen 2022 4 6181674 ???208094 = 1*479909#/5105103758926 12.9012 Jansen and Jens Kruse Andersen 2022 5 5198448 ???157490 = 363257*363269#/5105102177806 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#/300303166622 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#/96996902492758 13.5259 Jansen and Jens Kruse Andersen 2022 4 6181674 C?P208094 = 1*479909#/5105103758926 12.9012 Jansen and Jens Kruse Andersen 2022 5 5198448 C?P157490 = 363257*363269#/5105102177806 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 layout could you change gap 6181674 to 479909#/5105103758926 (instead of 1*479909#/5105103758926)? Kind regards Michiel 

20220413, 06:30  #85  
"Seth"
Apr 2019
19×23 Posts 
Quote:
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 primegaplistproject.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. 

20220413, 09:33  #86  
Einyen
Dec 2003
Denmark
D3B_{16} Posts 
Quote:


20220414, 21:51  #87 
Jan 2018
2×5×11 Posts 
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 
20220416, 00:01  #88 
Jan 2018
2×5×11 Posts 
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#/96996903531714 and 29*479909#/9699690+3654858 After presieving with all primes till 10^12 and PRPing 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, presieving 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 20220416 at 00:06 Reason: added number of digits 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime counting function records  D. B. Staple  Computer Science & Computational Number Theory  50  20201216 07:24 
records for primes  3.14159  Information & Answers  8  20181209 00:08 
Records for complete factorisation  BrianE  Math  25  20091216 21:40 
gmpecm records page question  yqiang  GMPECM  6  20070518 12:23 
Records in January  wblipp  ElevenSmooth  10  20040322 01:26 