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-   -   Top 50 gaps (https://www.mersenneforum.org/showthread.php?t=23498)

robert44444uk 2018-07-10 08:01

Top 50 gaps
 
We can extend the list given at [url]http://ntheory.org/gaps/top20.pl[/url], to cover the top 50 gaps at varying levels of prime gap length and merit. To qualify, a gap with a rank of 1 means that every gap found to be larger than the rank 1 gap has a smaller merit. I then rank the gaps larger than the rank 1 gap in order of merit and ignore those that are lower than 50th. I then rank the qualifying gaps according to their highest position. I only list gaps starting from 8350 which is the greatest merit gap. Of course, gaps that are not the top merit for their length are not included as there are no records kept of these gaps. The gap list used for this analysis is 3 July 2018 at [url]http://trnicely.net/index.html#TPG[/url]

As expected danaj dominates the Top 50 list but with less of a dominant percentage. Only 11 discoverers are on the list, and their discoveries cover 98% of all listed gaps.



[CODE]
Gapcoin 3 0.87% 849 0.92%
Jacobsen 166 48.40% 56773 61.68%
M.Jansen 27 7.87% 2559 2.78%
MJandJKA 2 0.58% 2 0.00%
MJPC&JKA 17 4.96% 2594 2.82%
MrtnRaab 28 8.16% 114 0.12%
PierCami 7 2.04% 789 0.86%
RobSmith 34 9.91% 7573 8.23%
Rosnthal 33 9.62% 10996 11.95%
RosntlJA 1 0.29% 8 0.01%
Toni_Key 25 7.29% 9793 10.64%

Total 343 100.00% 92050 100.00%
Total gaps 93945

97.98%
[/CODE]


[CODE]
Gap Merit Finder Hi rank 8350 15900 18306 26054 26892 66520 70862 71766 77640 120664 157178 309030 512226 1113106 1286500 2332764 4680156 6582144
8350 41.9388 Gapcoin 1 1
15900 39.6202 Jacobsen 1 2 1
18306 38.0670 Jacobsen 1 3 2 1
26054 37.0053 Jacobsen 1 5 3 2 1
26892 36.4206 Jacobsen 1 8 4 3 2 1
66520 35.4245 M.Jansen 1 16 9 8 4 2 1
70862 34.8067 Toni_Key 1 21 12 11 5 3 2 1
71766 34.4576 Jacobsen 1 34 19 18 8 6 3 2 1
77640 32.6483 Toni_Key 1 20 16 4 3 2 1
120664 32.3245 MJPC&JKA 1 27 23 7 5 3 2 1
157178 31.8285 Jacobsen 1 41 36 9 7 5 4 2 1
309030 31.7822 Rosnthal 1 44 39 10 8 6 5 3 2 1
512226 29.7175 RobSmith 1 29 22 20 16 7 5 2 1
1113106 25.9045 MJPC&JKA 1 4 2 1
1286500 25.8571 Rosnthal 1 5 3 2 1
2332764 25.7927 MrtnRaab 1 6 4 3 2 1
4680156 20.3767 MrtnRaab 1 33 5 4 3 2 1
6582144 13.1829 MrtnRaab 1 5 4 3 2 1
26730 35.7817 Jacobsen 3 11 6 5 3
109776 32.2502 Jacobsen 3 30 25 8 6 4 3
157194 30.3829 RobSmith 3 18 14 12 10 5 3
379304 26.3114 RobSmith 3 43 3
5103138 10.2203 RobSmith 3 6 5 4 3
8382 37.8241 Jacobsen 4 4
24416 36.0241 Jacobsen 4 9 5 4
27340 34.7080 Jacobsen 4 24 14 13 6 4
71046 32.5590 Jacobsen 4 21 17 5 4
125078 30.4885 Jacobsen 4 17 13 11 9 4
286764 29.7946 Rosnthal 4 25 19 17 14 6 4
3311852 14.6838 MJandJKA 5 7 6 5
27666 34.6593 Gapcoin 5 28 16 15 7 5
2079500 22.9896 MrtnRaab 6 14 6 8 7
2945060 12.8223 MrtnRaab 6 9 8 6
10716 36.8583 Jacobsen 6 6
24818 35.5799 Jacobsen 6 13 7 6
68202 32.4219 Toni_Key 6 25 21 6
101616 30.8124 Jacobsen 6 14 10 8 6
193396 29.5530 Toni_Key 6 32 24 22 18 8 6
3870360 12.4164 RobSmith 7 10 9 7
1260182 25.3279 Rosnthal 7 7 7 11
13692 36.5902 Jacobsen 7 7
23548 35.4249 Jacobsen 7 15 8 7
42242 34.1987 Jacobsen 7 43 21 20 9 7
76606 31.4202 Jacobsen 7 12 9 7
84766 30.7110 Jacobsen 7 15 11 9 7
280364 29.1570 Toni_Key 7 40 32 29 23 9 7
2765878 12.0114 MJPC&JKA 8 12 10 8
1151150 23.1376 Rosnthal 8 13 8 13
984108 25.2886 M.Jansen 8 8 9
29620 33.5751 Jacobsen 8 32 31 11 8
99160 30.5264 Jacobsen 8 16 12 10 8
179548 28.6615 Jacobsen 8 45 41 32 10 8
2724214 11.8311 MJandJKA 9 14 11 9
19474 35.1999 Jacobsen 9 17 10 9
35004 33.5011 Jacobsen 9 34 33 12 9
165894 28.6020 Toni_Key 9 49 45 35 11 9
321562 24.5692 Toni_Key 9 9
3370374 11.2705 MrtnRaab 10 15 12 10
566040 23.5278 M.Jansen 10 11 10
9006 35.8500 Jacobsen 10 10
24008 34.9648 Jacobsen 10 18 11 10
26858 33.6621 Gapcoin 10 27 26 10
60310 33.2174 Jacobsen 10 48 44 14 10
262726 28.5665 Rosnthal 10 47 36 12 10
418250 23.5527 RobSmith 10 10
2586246 11.2601 MrtnRaab 11 16 13 11
1113976 22.3878 Rosnthal 11 16 11 17
51510 33.0719 Toni_Key 11 49 15 11
69802 31.4615 Jacobsen 11 50 11
116676 30.3614 Toni_Key 11 19 15 13 11
278508 28.4694 Rosnthal 11 41 15 11
2559528 11.1438 MrtnRaab 12 18 14 12
973764 22.6787 MJPC&JKA 12 15 12
13024 35.6819 Jacobsen 12 12
18840 34.7563 Jacobsen 12 22 13 12
55982 33.0628 Jacobsen 12 50 16 12
85686 30.0930 MJPC&JKA 12 22 17 15 12
265242 28.1789 Toni_Key 12 49 18 12
383796 23.2066 PierCami 12 12
2493532 10.8564 MrtnRaab 13 19 15 13
535836 22.0188 Jacobsen 13 19 13
26250 33.3265 Jacobsen 13 41 39 13
27480 32.8594 Jacobsen 13 17 13
66816 30.9578 Jacobsen 13 13
86934 29.9766 MJPC&JKA 13 23 18 16 13
131574 28.5033 Jacobsen 13 39 13
209912 28.1022 RobSmith 13 19 13
1521800 16.7563 MrtnRaab 16 20 16
2435476 10.6037 MrtnRaab 14 21 17 14
834114 21.9588 M.Jansen 14 20 14
11924 35.4550 Jacobsen 14 14
19170 34.6876 Jacobsen 14 26 15 14
63524 32.7941 Jacobsen 14 18 14
73200 30.1202 Jacobsen 14 21 16 14
135182 28.5001 Jacobsen 14 40 14
189570 28.0088 RobSmith 14 20 14
538328 21.8527 M.Jansen 15 22 15
30096 32.6764 Jacobsen 15 19 15
82478 29.7727 Toni_Key 15 27 21 19 15
173800 27.7067 Jacobsen 15 25 15
1084830 21.8035 Rosnthal 16 23 16
21126 34.6177 Jacobsen 16 29 17 16
146856 28.3319 M.Jansen 16 45 16
270602 27.7045 Rosnthal 16 27 16
1069640 21.4978 Rosnthal 17 25 17
22040 34.5159 Jacobsen 17 31 18 17
101028 29.6477 RobSmith 17 31 23 21 17
135232 28.1928 Jacobsen 17 48 17
226278 27.6144 Jacobsen 17 29 17
384902 22.3707 M.Jansen 17 17
1471730 16.2111 MrtnRaab 18 22 18
1045498 21.0130 Rosnthal 18 27 18
37854 32.5151 Jacobsen 18 22 18
77256 29.7857 Jacobsen 18 26 20 18
258246 27.5751 Rosnthal 18 32 18
324618 22.3122 M.Jansen 18 18
1462522 16.1016 MrtnRaab 19 23 19
818886 20.8333 M.Jansen 19 31 19
10942 34.9114 Jacobsen 19 19
23812 34.2766 Jacobsen 19 40 20 19
35960 32.4712 Jacobsen 19 23 19
80774 29.4589 Jacobsen 19 35 27 24 19
272586 27.5724 Rosnthal 19 33 19
2055816 15.6743 PierCami 20 24 20
12742 34.8525 Jacobsen 20 20
39408 32.4472 Jacobsen 20 24 20
67370 30.3467 Jacobsen 20 20
82640 29.4473 Jacobsen 20 36 28 25 20
222854 27.5377 Toni_Key 20 34 20
1004840 20.1968 Rosnthal 20 36 20
1419558 15.6620 MrtnRaab 21 25 21
22704 34.1509 Jacobsen 21 44 22 21
91644 29.2970 Jacobsen 21 37 29 26 21
128130 27.9402 MJPC&JKA 21 21
213780 27.3088 RobSmith 21 35 21
322982 21.8674 Toni_Key 21 21
1004972 20.1966 Rosnthal 21 37 21
1417014 15.6246 MrtnRaab 22 26 22
23790 34.1236 Jacobsen 22 45 23 22
36810 32.3930 Jacobsen 22 26 22
104094 29.2142 MJPC&JKA 22 39 31 28 22
143692 27.8323 MJPC&JKA 22 22
228294 27.2609 Toni_Key 22 36 22
865056 20.1598 PierCami 22 38 22
1390164 15.3242 MrtnRaab 23 27 23
11350 34.7489 Jacobsen 23 23
25408 34.0084 Jacobsen 23 48 24 23
73294 29.5056 Jacobsen 23 33 25 23
129220 27.8286 MJPC&JKA 23 23
162762 27.2304 Jacobsen 23 37 23
1002890 20.1556 Rosnthal 23 39 23
1386416 15.3176 MrtnRaab 24 28 24
22352 33.7498 Jacobsen 24 25 24
46410 32.3200 Jacobsen 24 28 24
66720 29.8466 Jacobsen 24 24
80346 29.1252 Jacobsen 24 42 33 30 24
155808 27.7981 Jacobsen 24 24
250608 27.2170 Rosnthal 24 38 24
338362 21.7854 RobSmith 24 24
784246 20.0601 M.Jansen 24 42 24
1575828 15.0964 M.Jansen 25 29 25
13720 34.7057 Jacobsen 25 25
21300 33.7115 Jacobsen 25 26 25
99868 29.0583 Jacobsen 25 43 34 31 25
194460 27.1662 RobSmith 25 39 25
997164 20.0410 Rosnthal 25 44 25
1321710 14.6129 MrtnRaab 26 30 26
50866 32.2207 Jacobsen 26 31 26
71054 29.4620 Jacobsen 26 34 26
90928 29.0154 MJPC&JKA 26 44 35 32 26
125764 27.7064 Jacobsen 26 26
225082 27.0851 Toni_Key 26 42 26
365540 21.2069 RobSmith 26 26
571948 20.0142 Jacobsen 26 45 26
1452592 14.5724 RobSmith 27 31 27
13704 34.6818 Jacobsen 27 27
25068 33.6132 Jacobsen 27 28 27
30450 32.2155 Jacobsen 27 32 27
72776 29.2839 Jacobsen 27 38 30 27
85242 28.9713 Jacobsen 27 46 37 34 27
167332 27.0564 Jacobsen 27 43 27
540598 19.9971 M.Jansen 27 47 27
1289448 14.2096 MrtnRaab 28 32 28
22474 33.6102 Jacobsen 28 29 28
37816 32.0958 Jacobsen 28 33 28
70278 29.7625 Jacobsen 28 28
79698 28.7625 MJPC&JKA 28 41 37 28
126030 27.6148 Jacobsen 28 28
170316 27.0345 Jacobsen 28 44 28
360610 20.9216 RobSmith 28 28
993888 19.9768 Rosnthal 28 49 28
1289022 14.1924 MrtnRaab 29 33 29
24412 33.6052 Jacobsen 29 30 29
26592 32.2772 Jacobsen 29 29
37786 32.0556 Jacobsen 29 34 29
79578 28.7620 Toni_Key 29 42 38 29
263574 27.0324 Rosnthal 29 45 29
360054 20.8890 RobSmith 29 29
809952 19.9443 M.Jansen 29 50 29
1398354 13.3957 RobSmith 30 34 30
12176 34.6060 Jacobsen 30 30
19332 33.6048 RobSmith 30 31 30
39534 31.9988 Jacobsen 30 35 30
66586 29.6835 Jacobsen 30 30
109084 28.7413 Jacobsen 30 43 39 30
128960 27.6038 Jacobsen 30 30
263648 27.0229 Rosnthal 30 46 30
326404 20.8574 M.Jansen 30 30
809574 19.8675 M.Jansen 30 30
2254930 11.2755 RosntlJA 31 35 31
61578 31.9635 Toni_Key 31 36 31
89692 28.6818 Jacobsen 31 44 40 31
129532 27.5785 Toni_Key 31 31
174864 26.9739 Toni_Key 31 47 31
679690 19.7981 M.Jansen 31 31
9030 34.5090 Jacobsen 32 32
25056 33.5059 Jacobsen 32 33 32
35418 31.9591 Jacobsen 32 37 32
254622 26.8202 Rosnthal 32 48 32
358374 20.5309 M.Jansen 32 32
875274 19.7343 PierCami 32 32
2218822 7.1182 RobSmith 32 36 32
14614 34.4755 Jacobsen 33 33
51942 31.8854 Jacobsen 33 38 33
77514 29.0041 Jacobsen 33 45 36 33
93570 28.6498 Jacobsen 33 46 42 33
211044 26.7366 Jacobsen 33 50 33
618480 19.7317 M.Jansen 33 33
1569660 7.0001 M.Jansen 33 37 33
18954 33.4915 Jacobsen 34 35 34
40710 31.8627 Jacobsen 34 39 34
96948 28.6249 Jacobsen 34 48 44 34
246356 26.6965 Rosnthal 34 34
318876 20.3669 M.Jansen 34 34
843888 19.6665 PierCami 34 34
2028240 6.5068 RobSmith 34 38 34
11570 34.3835 Jacobsen 35 35
20004 33.4838 Jacobsen 35 36 35
29804 31.8444 Jacobsen 35 40 35
74980 28.9459 MJPC&JKA 35 47 38 35
282702 26.6546 RobSmith 35 35
342336 20.3206 Jacobsen 35 35
967630 19.4470 Rosnthal 35 35
13112 34.3477 Jacobsen 36 36
18508 33.4563 Jacobsen 36 37 36
73722 28.8584 Jacobsen 36 48 39 36
252708 26.6447 Rosnthal 36 36
546518 19.4101 Jacobsen 36 36
10924 34.3072 Jacobsen 37 37
22136 33.4436 Jacobsen 37 38 37
37052 31.8213 Jacobsen 37 42 37
89460 28.5636 Jacobsen 37 48 37
181230 26.6431 Toni_Key 37 37
830202 19.3475 PierCami 37 37
12510 34.3038 Jacobsen 38 38
22364 33.4404 Jacobsen 38 39 38
31146 31.8206 Jacobsen 38 43 38
84234 28.5480 Jacobsen 38 49 38
189604 26.4933 Toni_Key 38 38
707970 19.3071 M.Jansen 38 38
1284234 14.1659 MrtnRaab 39 39
14028 34.2893 Jacobsen 39 39
176900 26.4883 Jacobsen 39 39
960492 19.3044 Rosnthal 39 39
1217460 13.4036 MrtnRaab 40 40
17396 33.4121 Jacobsen 40 40
23802 33.3047 Jacobsen 40 43 40
38784 31.7367 Jacobsen 40 45 40
71704 28.8164 MJPC&JKA 40 40
131376 27.1415 RobSmith 40 40
280566 26.4701 RobSmith 40 40
360072 20.0760 RobSmith 40 40
826800 19.2463 MJPC&JKA 40 40
1212942 13.3981 MrtnRaab 41 41
9370 34.2712 Jacobsen 41 41
21674 33.2910 Jacobsen 41 44 41
33160 31.7327 Jacobsen 41 46 41
70284 29.1308 Jacobsen 41 41
140640 27.0857 Jacobsen 41 41
251404 26.4034 Rosnthal 41 41
333906 20.0698 RobSmith 41 41
953940 19.1715 Rosnthal 41 41
1216548 13.3919 MrtnRaab 42 42
11868 34.2280 Jacobsen 42 42
17374 33.3091 Jacobsen 42 42
25116 33.2776 M.Jansen 42 45 42
62110 31.6880 Toni_Key 42 47 42
97724 28.3876 Jacobsen 42 42
237250 26.3139 Rosnthal 42 42
622560 19.1515 M.Jansen 42 42
1176666 12.9561 MrtnRaab 43 43
21318 33.2557 Jacobsen 43 46 43
44720 31.6591 Jacobsen 43 48 43
73116 28.6311 Jacobsen 43 47 43
93228 28.3660 Jacobsen 43 43
440020 20.0600 Jacobsen 43 43
756258 19.0704 M.Jansen 43 43
1158992 12.7816 MrtnRaab 44 44
34804 31.6366 Jacobsen 44 49 44
101878 28.3555 MJPC&JKA 44 44
159262 26.2755 Toni_Key 44 44
571356 19.0057 M.Jansen 44 44
1150108 12.6876 MrtnRaab 45 45
22400 33.2046 Jacobsen 45 50 45
33008 31.5838 Jacobsen 45 50 45
212252 26.1934 Toni_Key 45 45
856608 18.9608 PierCami 45 45
1134502 12.5131 MrtnRaab 46 46
11160 34.1091 Jacobsen 46 46
25888 33.1558 Jacobsen 46 46
38118 31.5712 Jacobsen 46 46
72954 28.5694 Jacobsen 46 50 46
95312 28.3233 Jacobsen 46 46
298728 26.1667 RobSmith 46 46
312154 20.0025 Jacobsen 46 46
942304 18.9389 Rosnthal 46 46
1224222 12.2811 RobSmith 47 47
10442 34.0379 Jacobsen 47 47
18180 33.2269 Jacobsen 47 47
23116 33.1377 Jacobsen 47 47
36920 31.5137 Jacobsen 47 47
88530 28.3034 MJPC&JKA 47 47
160330 26.1316 RobSmith 47 47
788542 18.8448 M.Jansen 47 47
1117820 11.2141 RobSmith 48 48
20076 33.0978 Jacobsen 48 48
54880 31.5118 RobSmith 48 48
165604 26.1050 RobSmith 48 48
316982 19.9865 RobSmith 48 48
935950 18.8099 Rosnthal 48 48
11382 33.9128 Jacobsen 49 49
17376 33.2151 Jacobsen 49 49
62724 31.5065 Jacobsen 49 49
69840 28.8561 Jacobsen 49 49
154202 26.8129 Toni_Key 49 49
210268 26.0915 RobSmith 49 49
599040 18.7943 M.Jansen 49 49
13782 33.8980 Jacobsen 50 50
68540 28.8546 Jacobsen 50 50
75848 28.5089 Jacobsen 50 50
93786 28.1763 Jacobsen 50 50
174150 26.0706 RobSmith 50 50
931870 18.7279 Rosnthal 50 50


[/CODE]

danaj 2018-07-10 20:50

[url]http://ntheory.org/gaps/top50.pl[/url]

The first line of the top20.pl file is "$top = 20;" so it was a rather trivial change. Really it should just take an optional argument, e.g. "top20.pl?top=50".


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