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2021-06-04, 20:25   #254
ATH
Einyen

Dec 2003
Denmark

3,251 Posts

Quote:
 Originally Posted by mart_r The other gap finally got empocketed this morning. 4397298 19.6406 224423#/107371994730-2375864
Gap verified. Endpoints:

Code:
224423#/107371994730-2375864+0 is Lucas PRP! (573.4657s+0.0420s)
224423#/107371994730-2375864+0 is 31-PRP! (158.3670s+0.0416s)
224423#/107371994730-2375864+0 is 61-PRP! (153.6002s+0.0383s)
224423#/107371994730-2375864+0 is 89-PRP! (151.6521s+0.0389s)
224423#/107371994730-2375864+0 is 107-PRP! (152.2096s+0.0395s)
224423#/107371994730-2375864+0 is 127-PRP! (152.4766s+0.0384s)

224423#/107371994730-2375864+4397298 is Lucas PRP! (588.1537s+0.0406s)
224423#/107371994730-2375864+4397298 is 31-PRP! (155.4292s+0.0398s)
224423#/107371994730-2375864+4397298 is 61-PRP! (152.4790s+0.0404s)
224423#/107371994730-2375864+4397298 is 89-PRP! (154.3925s+0.0398s)
224423#/107371994730-2375864+4397298 is 107-PRP! (152.6616s+0.0402s)
224423#/107371994730-2375864+4397298 is 127-PRP! (154.4092s+0.0402s)
2,168,869 factors and 29,779 composite PRP tests: primegap4397298.zip (Use 7-zip)

Last fiddled with by ATH on 2021-06-04 at 20:44

2021-06-04, 20:56   #255
SethTro

"Seth"
Apr 2019

409 Posts

Quote:
 Originally Posted by ATH Gap verified.

Thank you ATH for verifying these! I manually entered them (always a little scary) and pushed to the GitHub repository just now (commit 3dfd00de)

I'll update the wiki site on next week

 2021-06-06, 10:59 #256 mart_r     Dec 2008 you know...around... 13028 Posts Many many thanks ATH! My next gaps will be smaller in both number size and gap size.
 2021-06-11, 08:55 #257 SethTro     "Seth" Apr 2019 40910 Posts Couple of updates Craig did it again! They submitted the fifth largest gap by merit a 38.2 merit record! They now have the 3rd, 4th, and 5th largest merit records! Martin added three Megagaps (gap > 1,000,000), thanks ATH for verifying these. We continue to submit new records and improvements at a breakneck pace; 23,130 so far this year! This is more records than we have remaining from 2017 (the highest other year). The average merit of these records is ~22.1! (the median merit of all records is 19.48) Last fiddled with by SethTro on 2021-06-11 at 08:55
 2021-06-19, 09:14 #258 robert44444uk     Jun 2003 Oxford, UK 37408 Posts It will be interesting to see how these facts on prime gaps change over the next year: As of the most recent list, the lowest gap size with no known prime pair is 113326. The 10th smallest such gap is 124106 The 100th smallest such gap is 137966 The 1000th smallest such gap is 156288 The 10000th smallest such gap is 198692 I expect the 10000th will soon be over 200000
 2021-07-28, 15:19 #259 robert44444uk     Jun 2003 Oxford, UK 25·32·7 Posts This was the "most wanted" gap with no known pair of primes! 113326 11.5806 62857*9859#/46410-57330 119222 will now be the smallest missing gap in the table. Last fiddled with by robert44444uk on 2021-07-28 at 15:20
 2021-08-06, 17:15 #260 robert44444uk     Jun 2003 Oxford, UK 25×32×7 Posts Continuing my good fortune - here is the lower prime of the largest merit 30 gap found to date 313842 31.886 343921*9923#/46410-205340 This narrowly beats out Hans Rosenthal's 2015 find: 309030 31.782 1111111111111111111*9787#/(7#*641) - 130308
 2021-08-12, 12:56 #261 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 174016 Posts I have just submitted my first 30 merit gap: Code: 90240 30.742 47193529 * 2999#/2303070 -50488 to +39752 This knocks two gaps off https://primegap-list-project.github...gh-watermarks/
2021-09-09, 20:15   #262
mart_r

Dec 2008
you know...around...

2×353 Posts
arXiv news

Quote:
 It is proven that there are infinitely prime pairs whose difference is no greater than 20.
https://arxiv.org/abs/2109.03681

I'm not quite convinced yet, even if I only understand rather little of the paper. Especially, on page 3, the set H = {0, 2, 6, 8, 12, 14, 18, 20} is not admissible. Omit the 14, then it works.
Achieving the result quoted without Elliott-Halberstamm or something similar would be quite big news. Any thoughts?

 2021-11-02, 08:47 #263 robert44444uk     Jun 2003 Oxford, UK 25·32·7 Posts Here is a nice gap, found yesterday - not a record breaker - but my first 35 merit for a while 72350 35.502 32960023 * 2087#/46410 -30026 to +42324
2021-11-03, 18:52   #264
MJansen

Jan 2018

1258 Posts

Quote:
 Originally Posted by robert44444uk Here is a nice gap, found yesterday - not a record breaker - but my first 35 merit for a while 72350 35.502 32960023 * 2087#/46410 -30026 to +42324
Congrats, indeed a nice one! Have you moved to GPU coding or just to a Unix variant under WSL2? You seem to find more and more gaps over 40.000 these last days?

Kind regards
Michiel

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