Prime Gap News

[ATH]

Originally Posted by mart_r

The other gap finally got empocketed this morning.
4397298 19.6406 224423#/107371994730-2375864

Gap verified. Endpoints:

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)

[SethTro]

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

[mart_r]

Many many thanks ATH!

My next gaps will be smaller in both number size and gap size.

[SethTro]

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)

[robert44444uk]

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

[robert44444uk]

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.

[robert44444uk]

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

[henryzz]

I have just submitted my first 30 merit gap:

90240  30.742  47193529 * 2999#/2303070 -50488 to +39752

This knocks two gaps off https://primegap-list-project.github...gh-watermarks/

[mart_r]

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?

[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

[MJansen]

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