The Top-20 Prime Gaps for all merits

This page shows all prime gaps which are among the 20 largest known gaps with at least that merit, where merit = size / ln(gap start).
The table may be updated less frequently than The Top-20 Prime Gaps.
Example of possible entry:
Rank Size Gap start Merit Discoverer Year
6 43466 P847 = 2162932589... 22.3045 Torbjörn Alm & Jens K. Andersen 2006
This shows a gap of 43466 with merit 22.3045, between 847-digit primes. The rank 6 means it is the 6th largest known gap with merit ≥ 22.3045. In other words, there are 5 known gaps which are both larger and have higher merit.
For any m, the top-20 known gaps with merit > m are the first 20 listed gaps with merit > m, regardless of their listed rank.
If this table is up to date, it includes all top-20 gaps on the other page, but the listed ranks are often different because they rank different things.

 

Gaps which are among the 20 largest with at least that merit
Rank Size Gap start Merit Discoverer Year
1 2254930 PRP86853 = 1122483511... 11.28     Hans Rosenthal & Jens K. Andersen 2004
1 1078180 PRP38007 = 50491*(87811#)/6 - 657714 12.32     Pierre Cami 2006
3 1001548 PRP43429 = 1913094464... 10.0157 Hans Rosenthal & Jens K. Andersen 2004
2 825658 PRP29317 = 51307*(67777#)/6 - 327676 12.23     Pierre Cami 2006
1 800676 PRP20045 = 25175*(464... 17.35     Pierre Cami 2010
5 725724 PRP31103 = 10^31103 - 86991 10.13     Patrick De Geest 2008
4 724248 PRP26002 = 51257*(60037#)/6 - 411266 12.10     Pierre Cami 2007
2 675034 PRP21717 = 1872591871... 13.4997 Hans Rosenthal & Jens K. Andersen 2003
4 613744 PRP21718 = 2161936776... 12.2734 Hans Rosenthal & Jens K. Andersen 2003
7 565072 PRP21718 = 2080425850... 11.3001 Hans Rosenthal & Jens K. Andersen 2003
9 561186 PRP21718 = 1802254367... 11.2224 Hans Rosenthal & Jens K. Andersen 2003
10 506634 PRP21718 = 2054644885... 10.1315 Hans Rosenthal & Jens K. Andersen 2003
2 411584 PRP12925 = 7*(30011#)/6 - 155222 13.83     Arkadiusz Wesolowski 2009
7 398370 PRP14173 = 10^14173 - 51197 12.21     Milton L. Brown 2007
1 383796 PRP7183 = 9527*(1667... 23.21     Pierre Cami 2010
3 366984 PRP10003 = 1240467652... 15.9346 Jens K. Andersen 2009
2 351526 P7984 = 15889*(18481#)/6 - 197044 19.12     Pierre Cami 2009
5 338396 PRP10003 = 8510377399... 14.6920 Torbjörn Alm & Jens K. Andersen 2004
6 338178 PRP10000 = 1016538985... 14.6883 Jens K. Andersen 2009
3 337446 P7996 = 1009461925... 18.3303 Torbjörn Alm, Jens K. Andersen, François Morain 2004
4 332322 PRP7984 = 19577*(18481#)/6 - 235964 18.08     Pierre Cami 2009
5 329970 PRP8009 = 9643*(18539#)/6 - 241796 17.89     Pierre Cami 2006
6 327272 PRP7984 = 13831*(18481#)/6 - 145686 17.80     Pierre Cami 2009
2 325572 PRP7259 = 9529*(1688... 19.48     Pierre Cami 2010
2 303670 PRP6600 = 7121*(15319#)/210 - 208002 19.98     Pierre Cami 2009
10 302520 PRP7748 = 2028107417... 16.9585 Torbjörn Alm & Jens K. Andersen 2007
16 299286 PRP10003 = 1159321388... 12.9951 Jens K. Andersen 2009
17 299114 PRP10003 = 1285329036... 12.9876 Jens K. Andersen 2009
11 298242 PRP7978 = 2157331*(1... 16.24     Pierre Cami 2006
19 293336 PRP10003 = 1002094899... 12.7369 Jens K. Andersen 2009
20 290684 PRP10003 = 1316413440... 12.6216 Jens K. Andersen 2009
13 289920 PRP8031 = 6985*(18593#)/6 - 131046 15.68     Pierre Cami 2007
14 289476 PRP8030 = 6835*(18593#)/6 - 135638 15.66     Pierre Cami 2007
12 289170 PRP7748 = 2615317689... 16.2099 Torbjörn Alm & Jens K. Andersen 2007
16 287968 PRP8248 = 2643445728... 15.1639 Torbjörn Alm & Jens K. Andersen 2006
5 286566 PRP6533 = 8861*(15193#)/210 - 209288 19.05     Pierre Cami 2010
17 286200 PRP7984 = 6671*(18481#)/6 - 72902 15.57     Pierre Cami 2009
18 285862 PRP7984 = 12659*(18481#)/6 - 136014 15.55     Pierre Cami 2009
19 285096 PRP7984 = 9949*(18481#)/6 - 106558 15.51     Pierre Cami 2009
20 284412 PRP7982 = 485*(18481#)/6 - 180806 15.47     Pierre Cami 2009
7 283126 PRP6717 = 8839*(15583#)/210 - 138174 18.31     Pierre Cami 2010
8 278790 PRP6675 = 8839*(15473#)/210 - 169192 18.14     Pierre Cami 2010
17 277552 PRP7669 = 2101953105... 15.7191 Torbjörn Alm & Jens K. Andersen 2006
14 274872 PRP7266 = 373588081*... 16.43     Pierre Cami 2009
12 271166 PRP6675 = 7127*(15473#)/210 - 107612 17.64     Pierre Cami 2009
12 268702 PRP6575 = 9059*(15277#)/210 - 186306 17.75     Pierre Cami 2010
14 264060 PRP6537 = 8837*(15199#)/210 - 99074 17.54     Pierre Cami 2010
16 258356 PRP6612 = 7159*(15349#)/210 - 138218 16.97     Pierre Cami 2010
16 257244 PRP6520 = 7001*(15161#)/210 - 48946 17.14     Pierre Cami 2009
19 255462 PRP6713 = 9041*(15581#)/210 - 63604 16.53     Pierre Cami 2010
19 253136 PRP6545 = 7127*(15227#)/210 - 101562 16.80     Pierre Cami 2009
20 251256 PRP6537 = 7127*(15199#)/210 - 185714 16.69     Pierre Cami 2009
20 251022 PRP6528 = 7177*(15187#)/210 - 80074 16.70     Pierre Cami 2010
16 233822 P5878 = 1628253621... 17.2782 Jose Luis Gomez Pardo 2002
1 201832 P3379 = 14747*(7879#)/2310 - 65974 25.95     Pierre Cami 2010
2 189138 P3532 = 5077*(8243#)/210 - 59222 23.26     Pierre Cami 2010
4 181940 PRP3481 = 14699*(8123#)/210 - 51582 22.70     Pierre Cami 2010
4 178830 PRP3379 = 5569*(7879#)/210 - 103764 22.99     Pierre Cami 2010
6 173664 PRP3511 = 14633*(8219#)/2310 - 60934 21.48     Pierre Cami 2010
4 172860 P3263 = 9960696085... 23.0071 Jens K. Andersen 2009
8 171448 PRP3512 = 5171*(8219#)/210 - 118182 21.20     Pierre Cami 2010
8 165456 PRP3372 = 14543*(7873#)/210 - 77092 21.31     Pierre Cami 2010
10 162964 PRP3473 = 14537*(8111#)/210 - 61378 20.38     Pierre Cami 2010
10 162844 PRP3367 = 4967*(7867#)/210 - 101110 21.00     Pierre Cami 2010
11 162762 PRP3446 = 14549*(8059#)/210 - 89048 20.52     Pierre Cami 2010
14 159078 PRP3548 = 14737*(8287#)/210 - 60094 19.48     Pierre Cami 2010
16 156784 PRP3531 = 4957*(8243#)/210 - 50682 19.28     Pierre Cami 2010
12 156552 PRP3336 = 5399*(7759#)/210 - 82690 20.38     Pierre Cami 2010
19 155940 PRP3547 = 14561*(8287#)/2310 - 61440 19.10     Pierre Cami 2010
18 155414 PRP3519 = 14669*(8231#)/2310 - 93356 19.18     Pierre Cami 2010
15 154082 PRP3367 = 4993*(7867#)/210 - 112082 19.87     Pierre Cami 2010
16 153114 PRP3359 = 14713*(7841#)/2310 - 31838 19.80     Pierre Cami 2010
20 152760 PRP3453 = 5581*(8081#)/210 - 53902 19.21     Pierre Cami 2010
19 152130 PRP3415 = 14537*(7951#)/210 - 89966 19.35     Pierre Cami 2010
14 150846 P3263 = 6641012271... 20.0782 Jens K. Andersen 2009
16 149864 PRP3263 = 6643985524... 19.9475 Jens K. Andersen 2009
17 149370 PRP3263 = 9961966276... 19.8807 Jens K. Andersen 2009
2 146286 P2527 = 3137*(5879#)/210 - 43702 25.14     Pierre Cami 2009
3 146154 PRP2693 = 317*(6287#)/210 - 55724 23.58     Pierre Cami 2010
13 134172 PRP2829 = 29*(6607#)/210 - 56698 20.60     Pierre Cami 2010
15 131696 PRP2803 = 317*(6553#)/210 - 117618 20.41     Pierre Cami 2010
18 128416 PRP2750 = 199*(6389#)/210 - 75598 20.29     Pierre Cami 2010
9 122566 P2392 = 319*(5591#)/6 - 88188 22.25     Pierre Cami 2009
19 120728 PRP2584 = 2969*(6047#)/210 - 73166 20.30     Pierre Cami 2009
9 114554 P2227 = 5787178675... 22.3419 Torbjörn Alm & Jens K. Andersen 2007
15 109680 P2289 = 6457*(5387#)/6 - 51928 20.81     Pierre Cami 2009
2 98498 PRP1688 = 1163*(3943#)/2310 - 42248 25.35     Pierre Cami 2010
15 96070 P1974 = 8492140607... 21.1369 Torbjörn Alm & Jens K. Andersen 2007
9 95920 PRP1814 = 943*(4243#)/2310 - 59482 22.97     Pierre Cami 2010
4 93620 PRP1707 = 2063*(4003#)/210 - 43874 23.82     Pierre Cami 2009
14 91360 PRP1799 = 985*(4219#)/30030 - 63634 22.06     Pierre Cami 2010
15 89502 PRP1810 = 1043*(4241#)/30030 - 55724 21.49     Pierre Cami 2010
4 89044 PRP1599 = 3547*(3739#)/2310 - 46570 24.19     Pierre Cami 2010
16 87768 PRP1773 = 965*(4153#)/30030 - 55122 21.50     Pierre Cami 2010
14 87378 PRP1704 = 241*(4003#)/30030 - 60446 22.27     Pierre Cami 2010
12 86634 PRP1656 = 815*(3881#)/2310 - 16076 22.73     Pierre Cami 2010
15 86630 PRP1687 = 809*(3943#)/30030 - 16418 22.31     Pierre Cami 2010
6 86152 PRP1587 = 1787*(3719#)/30030 - 61626 23.59     Pierre Cami 2010
17 85890 PRP1675 = 2971*(3919#)/210 - 46388 22.28     Pierre Cami 2009
6 85350 PRP1560 = 4007*(3659#)/2310 - 44852 23.77     Pierre Cami 2010
4 82238 P1447 = 3019*(3407#)/210 - 51236 24.69     Pierre Cami 2009
17 78966 PRP1529 = 2939*(3583#)/210 - 39502 22.44     Pierre Cami 2009
10 78016 P1443 = 3109*(3391#)/210 - 36970 23.48     Pierre Cami 2009
1 73874 P1209 = 2347*(2833#)/210 - 29658 26.54     Pierre Cami 2009
6 73660 P1298 = 5141*(3041#)/6 - 27358 24.66     Pierre Cami 2009
8 73464 PRP1329 = 2129*(3121#)/6 - 48702 24.02     Pierre Cami 2009
8 73464 P1329 = 2129*(3121#)/6 - 48702 24.02     Pierre Cami 2009
17 72102 P1359 = 3847*(3209#)/210 - 19354 23.05     Pierre Cami 2009
8 64416 P1165 = 3581*(2729#)/210 - 16022 24.03     Pierre Cami 2009
17 61902 PRP1158 = 3739*(2713#)/210 - 20742 23.23     Pierre Cami 2009
8 55248 PRP994 = 1013*(2347#)/210 - 35674 24.16     Pierre Cami 2009
2 49818 P828 = 1561504605... 26.1555 Torbjörn Alm & Jens K. Andersen 2004
4 44086 P746 = 2039666676... 25.6891 Torbjörn Alm & Jens K. Andersen 2004
16 40518 P743 = 1011682999... 23.7151 Torbjörn Alm & Jens K. Andersen 2007
9 40002 PRP710 = 1787*(1667#)/210 - 17684 24.48     Pierre Cami 2009
16 38232 P698 = 7876629104... 23.7914 Torbjörn Alm & Jens K. Andersen 2004
12 27750 P502 = 107641*(1187#)/6 - 15076 24.03     Pierre Cami 2009
10 24920 PRP445 = 17*(1061#)/210 - 8454 24.36     Pierre Cami 2009
9 19030 P338 = 1391395986... 24.5137 Torbjörn Alm & Jens K. Andersen 2006
18 16950 P309 = 8299419899... 23.8292 Torbjörn Alm & Jens K. Andersen 2004
12 13874 P249 = 9534435386... 24.2004 Torbjörn Alm & Jens K. Andersen 2003
19 12734 P232 = 1142983035... 23.9347 Torbjörn Alm & Jens K. Andersen 2006
2 12130 P201 = 2041957626... 26.2992 Torbjörn Alm & Jens K. Andersen 2004
6 11550 P196 = 5124283889... 25.6303 Jens K. Andersen 2003
9 11544 P201 = 2^666 + 4578280991763 25.01     Hans Rosenthal & Jim Fougeron 2008
12 11370 P201 = 2^666 + 1862281509553 24.63     Hans Rosenthal & Jim Fougeron 2008
13 11060 P196 = 6607162786... 24.5291 Jens K. Andersen 2003
10 11048 P194 = 6269182816... 24.7583 Jens K. Andersen 2003
10 10194 P179 = 1237970365... 24.8590 Torbjörn Alm & Jens K. Andersen 2004
2 10012 P165 = 1247358017... 26.4976 Torbjörn Alm & Jens K. Andersen 2007
20 9892 P178 = 2629790445... 24.2140 Torbjörn Alm & Jens K. Andersen 2006
8 9038 P154 = 4392874337... 25.5473 Torbjörn Alm & Jens K. Andersen 2006
5 8938 P149 = 2876050748... 26.1468 Torbjörn Alm & Jens K. Andersen 2007
9 8484 P145 = 1185529821... 25.5741 Jens K. Andersen 2003
13 8358 P145 = 373*(353#)/6 - 4622 25.08     Pierre Cami 2005
15 8268 P144 = 6839764161... 24.9643 Jens K. Andersen 2003
12 8118 P141 = 1598835071... 25.1463 Torbjörn Alm & Jens K. Andersen 2006
1 7868 P114 = 5611925455... 30.0400 Torbjörn Alm & Jens K. Andersen 2004
12 7614 P131 = 2^432 + 26350881366603 25.43     Hans Rosenthal & Jim Fougeron 2009
17 7516 P131 = 2432670075... 25.0346 Torbjörn Alm & Jens K. Andersen 2004
19 7382 P129 = 2205078866... 24.9796 Torbjörn Alm & Jens K. Andersen 2006
8 7200 P121 = 3414969343... 25.9424 Torbjörn Alm & Jens K. Andersen 2004
4 6802 P113 = 1513894229... 26.3333 Torbjörn Alm & Jens K. Andersen 2006
2 6700 P107 = 3675272035... 27.3051 Jens K. Andersen 2003
2 6380 P93 = 5629854038... 29.8737 Torbjörn Alm & Jens K. Andersen 2003
3 6372 P99 = 2391486495... 28.1293 Jens K. Andersen 2004
11 6286 P105 = 4772258873... 26.0796 Torbjörn Alm & Jens K. Andersen 2007
4 6252 P100 = 1947782222... 27.3464 Torbjörn Alm & Jens K. Andersen 2007
6 6126 P99 = 1930402313... 27.0689 Jens K. Andersen 2004
6 6112 P98 = 4179295430... 27.1909 Jens K. Andersen 2004
15 6072 P102 = 3424595617... 25.9718 Torbjörn Alm & Jens K. Andersen 2006
8 6006 P99 = 1587806676... 26.5616 Jens K. Andersen 2004
12 5972 P99 = 3383902638... 26.3232 Jens K. Andersen 2004
14 5950 P99 = 2075039196... 26.2829 Jens K. Andersen 2004
15 5924 P98 = 9098196578... 26.2637 Jens K. Andersen 2004
18 5876 P98 = 5310142458... 26.1132 Jens K. Andersen 2004
8 5470 P90 = 2^296 + 18607779589905 26.66     Hans Rosenthal & Jim Fougeron 2009
4 5454 P86 = 2780820016... 27.7215 Torbjörn Alm & Jens K. Andersen 2007
16 4494 P75 = 1802238158... 26.2837 Torbjörn Alm & Jens K. Andersen 2004
9 4188 P68 = 2563686469... 26.9820 Torbjörn Alm & Jens K. Andersen 2004
10 3762 P61 = 7588952269... 26.8366 Torbjörn Alm & Jens K. Andersen 2004
11 3732 P61 = 4896220058... 26.7061 Torbjörn Alm & Jens K. Andersen 2004
4 3652 P57 = 7372114533... 27.8901 Torbjörn Alm & Jens K. Andersen 2007
6 3348 P53 = 7445001821... 27.5008 Torbjörn Alm & Jens K. Andersen 2007
19 3334 P56 = 1010417611... 26.3240 Jens K. Andersen 2003
12 3180 P52 = 2880026500... 26.8378 Torbjörn Alm & Jens K. Andersen 2004
4 2976 P47 = 1294250293... 28.0287 Torbjörn Alm & Jens K. Andersen 2004
3 2936 P45 = 2894479986... 28.6784 Torbjörn Alm & Jens K. Andersen 2007
11 2660 P43 = 2256289111... 27.2758 Helmut Spielauer 2009
3 2442 P37 = 8611234000... 28.7138 Helmut Spielauer 2009
16 2422 P39 = 9998434894... 26.9708 Helmut Spielauer 2009
14 2310 P38 = 1002003004... 27.1134 Helmut Spielauer 2009
7 2250 P35 = 8174706997... 27.9889 Jens K. Andersen 2004
14 2248 P36 = 7391738820... 27.2185 Helmut Spielauer 2009
11 1858 P30 = 3198117140... 27.3487 Helmut Spielauer 2008
8 1836 P29 = 3481165400... 27.9368 Helmut Spielauer 2009
20 1770 P29 = 2961118100... 26.9990 Helmut Spielauer 2009
20 1700 P28 = 2021022000... 27.0385 Helmut Spielauer 2008
1 1476 P19 = 1425172824437699411 35.3103 Tomás Oliveira e Silva 2009
2 1442 P18 = 804212830686677669 34.9757 Siegfried Herzog & Tomás Oliveira e Silva 2005
3 1392 P19 = 1480032037939634731 33.2707 Tomás Oliveira e Silva 2009
3 1380 P19 = 1031501833130243273 33.2710 Siegfried Herzog & Tomás Oliveira e Silva 2007
3 1370 P18 = 418032645936712127 33.7652 Donald E. Knuth 2006
6 1364 P19 = 1051140888051230423 32.8703 Siegfried Herzog & Tomás Oliveira e Silva 2007
7 1362 P20 = 17847902862840722279 30.7252 Bertil Nyman 2009
7 1360 P19 = 1153277647303540597 32.7008 Siegfried Herzog & Tomás Oliveira e Silva 2008
4 1358 P18 = 523255220614645319 33.2853 Siegfried Herzog & Tomás Oliveira e Silva 2007
4 1356 P18 = 401429925999153707 33.4536 Donald E. Knuth 2006
10 1350 P19 = 1180351752204137089 32.4423 Tomás Oliveira e Silva 2008
10 1344 P18 = 753917635380895597 32.6498 Siegfried Herzog & Tomás Oliveira e Silva 2006
12 1342 P19 = 1578169106141187727 32.0265 Tomás Oliveira e Silva 2009
13 1340 P19 = 1954317467127310787 31.8165 Tomás Oliveira e Silva 2009
14 1332 P19 = 3995499983831331581 31.0985 Tomás Oliveira e Silva 2007
9 1328 P18 = 352521223451364323 32.8681 Tomás Oliveira e Silva 2006
18 1326 P20 = 17847776380021241051 29.9131 Bertil Nyman 2010
14 1322 P19 = 1106028436187467937 31.8191 Siegfried Herzog & Tomás Oliveira e Silva 2008
13 1320 P18 = 605046330029026447 32.2391 Siegfried Herzog & Tomás Oliveira e Silva 2006
17 1314 P19 = 1214119646547613277 31.5558 Tomás Oliveira e Silva 2008
18 1312 P19 = 1396487719253403577 31.4022 Siegfried Herzog & Tomás Oliveira e Silva 2009
19 1310 P19 = 1918586799657617591 31.1178 Tomás Oliveira e Silva 2009
17 1308 P18 = 749565457554371299 31.7798 Siegfried Herzog & Tomás Oliveira e Silva 2006
20 1304 P19 = 1188134379382395323 31.3319 Tomás Oliveira e Silva 2008
18 1292 P18 = 494653394305448051 31.7113 Tomás Oliveira e Silva 2006
19 1272 P18 = 305405826521087869 31.5943 Tomás Oliveira e Silva 2006
13 1132 P16 = 1693182318746371 32.2825 Bertil Nyman 1999

 

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Last updated 9 March 2010