Medium Gaps 60,000 to 500,000

[robert44444uk]

Originally Posted by danaj

Verification with either verify-primegaps.pl or cglp4 takes much longer. I used to have one machine running 8-processes non-stop for a week doing just verification of the gaps I was submitting. The small gaps are simple, it's the 12k digit ones that are a bear.

Hmm, that's good to know. Finding the records appears to be almost easy (I got 104 in the last 2 days on 4 cores, including 2 gaps where nothing is listed), Submitting them after cglp4 checking really does seem to tie the process up. I'll just have to start that process earlier.

[robert44444uk]

Whoa! 471 records this week. The field is really open. I managed to get three of the key blanks in the record, in the 67000's, but still 66718 (the lowest without an entry) is stubborn. I also improved 60182, the lowest with a merit of less than 10. 64038 is the lowest now.

I'm sorry to say Danaj, that 247 of these were your records. I do apologise, but I am sure you will have a plan to take them back.

Soon I will have enough records to appear on your graph!

[danaj]

Very nice!

I sent over 3500 new gaps last week, including one for 66718. Looks like 1100 new ones since then, though about 50% are improving my own. About 15% taking MJPC&JKA, 11% Rosenthal, 11% new, 7% M. Jansen.

That's funny that over half your records are ones from me.

[robert44444uk]

Originally Posted by danaj

That's funny that over half your records are ones from me.

That's because I am deep in territory owned by you!

I got a 67016 in the ones I am checking now, so it looks like the smallest is 67406 now unless your big submission had that as well.

[danaj]

As of the 2 July file, first gaps with no current record (merits following if I've found since):

62630
66718 12.54
67016 16.98
67406
67450
67544
67750
67814
67850
68110 16.11
68594
68606
68642
...

Low values:

60182 8.25 -> 12.71
63106 9.83 -> 12.83
63748 9.69 -> 13.32
63808 7.92 -> 11.86
64136 9.53
64298 9.93 -> 12.16
64382 8.20 -> 12.60
64954 8.50
65216 8.36
65398 3.96 (!)
65552 3.44 -> 12.52
65618 7.44
66182 8.996

Some improvements there, and it looks like 64136 the next one needing improvement (though 62630 is lower and has no entry). A couple of those have merit 3 which is pretty crazy. One got bumped up, but the other is still there. There are more of these lowball values in the 70k range, including 70294 with merit 2.90. At first I limited my submissions to higher merits, but now I submit them regardless since they can just get improved later.

[robert44444uk]

Hmm, I don't know why I missed the 62630, but I am now out of the range for finding that with 10+ merit.

In the batch I am checking now for submission I will claim the following gaps

67544 10.87
67850 10.80
68594 11.36
68606 11.60

Other low first time gaps in the late 60's and 70s I will be claiming
69124
69262
69314
70090
70636
70822
70984
72874
72986
73442
75118
75284
75286
75976
76066
76670
77438
77468
77542

And small current records improved:

73742 5.06 >> 12.36
75664 3.11 >> 13.44
76352 3.81 >> 13.36
76862 5.49 >> 12.66
78518 3.46 >> 13.29
79424 4.32 >> 12.37
79834 5.39 >> 12.92

[robert44444uk]

Three weeks in to this exercise and I have almost caught up with Gapcoin. The latest list of prime gaps has the "hit parade" of records as:

Jacobsen	35196
Rosnthal	10891
MJPC&JKA	8386
M.Jansen	5926
Spielaur	2682
PierCami	1952
Gapcoin-	1136
RobSmith	1006
TorAlmJA	835
Andersen	190
Be.Nyman	121
RP.Brent	120

[danaj]

Gaps with no merit or low merits from 1000 to 100000:

20140110: 7804 merit zero, 9486 merit < 10
20150104: 4044 merit zero, 5721 merit < 10
20150717: 1528 merit zero, 3569 merit < 10

I've got another 89 holes filled in the last couple weeks, and 276 raised over 10. I imagine you have some also.

Gapcoin looks like it is finding about 2 new gaps per day, even with the new miner. I'm finding over twice that many in the same range (gap length under 20k).

So far my records are ~50% my own, about 10% no-previous-record, 2.6% Robert Smith, and 0.5% Gapcoin. 9 new top-20 values (Robert, I see you have two in that list now -- the updated version of this).

I'll probably wait another couple weeks before sending, and it's been taking a bit over a week before posting (probably because the large sizes take a long time to verify).



I'm not nearly as convinced of the scientific merit of this exercise as the gapcoin PR is. I think it's an interesting puzzle, and a great exercise to prod me to write software, but I just am not seeing the mathematical benefit of finding non-true maximal gaps. On the other hand, it seems about as useful as looking for Mersenne primes which lots of people find a worthwhile use of their resources.

[robert44444uk]

Originally Posted by danaj

Gaps with no merit or low merits from 1000 to 100000:

20140110: 7804 merit zero, 9486 merit < 10
20150104: 4044 merit zero, 5721 merit < 10
20150717: 1528 merit zero, 3569 merit < 10

I've got another 89 holes filled in the last couple weeks, and 276 raised over 10. I imagine you have some also.


So far my records are ~50% my own, about 10% no-previous-record, 2.6% Robert Smith, and 0.5% Gapcoin. 9 new top-20 values (Robert, I see you have two in that list now -- the updated version of this).

I'll probably wait another couple weeks before sending, and it's been taking a bit over a week before posting (probably because the large sizes take a long time to verify).

I am making some inroads! My big batch last week contained about 50 first time gaps under 100k and the removal of about the same number of gap <100k which are <10 merit.

Since then I have the following small gaps done: 68642 and 70570 and one improved to over 10: 68014

A nice big juicy first timer this morning: 24.963327 111512 PRP1941 = 787*4549#/46410-37938

My current drive is about to enter the phase of maximum discovery in the small missing gap territory: at about 4700# to 5500#

A small problem with the top 20 list is that gaps that were never earliest occurrence are probably not being picked up at all.

[robert44444uk]

Originally Posted by danaj

Gaps with no merit or low merits from 1000 to 100000:

20150717: 1528 merit zero, 3569 merit < 10

I just submitted my weekly list with the following zero merits claimed:

60-70,000	1
70-80.000	26
80-90,000	8
90-100,000	9
100-110,000	7
110-120,000	8
120-130,000	5
130-140,000	1
140-150,000	0
	
60-100,000	44

And the following improved to >10

60-70,000	3
70-80.000	11
80-90,000	23
90-100,000	19
100-110,000	3
110-120,000	2
120-130,000	1
130-140,000	0
140-150,000	0
	
60-100,000	56

[danaj]

I sent mine yesterday as well. 136 gaps in the range 60k-100k with no previous merit, 384 improved to > 10 (including the zero merits). In all ranges, 396 total new gaps, 660 improved to > 10.

Ranges for the 396 new gaps: 4 60k-70k, 45 70k-80k, 43 80k-90k, 44 90k-100k, 44 100k-110k, 32 110k-120k, 24 120k-130k, 5 130k-140k, 10 140k-150k, 25 150k-200k, 78 200k-300k, 35 300k+.

Summary of the previous holders:

1693 48.9% Jacobsen
432 12.5% Rosnthal
432 12.5% MJPC&JKA
396 11.4%
216 6.2% M.Jansen
95 2.7% PierCami
77 2.2% RobSmith
52 1.5% Spielaur
39 1.1% TorAlmJA
19 0.5% Gapcoin
6 0.2% Andersen
1 0.0% H.Dubner
1 0.0% JLGPardo

Best for the top-20 was a 4th place at 89692 (merit 28.6818), highest merit was 31.56.

My double checking spent most of the time catching up with new entries and the dotted numbers, so is at 4301 digits. ECPP proving of all endpoints done through 1137 digits. I don't expect it to proceed much farther. Both are to the point where much more progress is going to require more than 1/8th each of a 4770k, and are also in the range where other tools are somewhat faster (OpenPFGW for the double checking of interior points, and Primo for the gap endpoints). Lots of their time is spent just catching up with new records.