| Pattern d: d = 0, 2 | ||||||
|
merit = 1.32032363 ·∫dt / log2 t Gap start | Rank | Gap Size | Gap start | Next Twin Prime | Merit | Who | When |
| 1 | 2 | 3 | 5 | 1.445810 | Randall L. Rathbun | 1998 |
| 2 | 6 | 5 | 11 | 1.948453 | Randall L. Rathbun | 1998 |
| 3 | 12 | 17 | 29 | 1.635470 | Randall L. Rathbun | 1998 |
| 4 | 18 | 41 | 59 | 1.560641 | Randall L. Rathbun | 1998 |
| 5 | 30 | 71 | 101 | 2.004066 | Randall L. Rathbun | 1998 |
| 6 | 36 | 311 | 347 | 1.415243 | Randall L. Rathbun | 1998 |
| 7 | 72 | 347 | 419 | 2.688998 | Randall L. Rathbun | 1998 |
| 8 | 150 | 659 | 809 | 4.552129 | Randall L. Rathbun | 1998 |
| 9 | 168 | 2381 | 2549 | 3.636832 | Randall L. Rathbun | 1998 |
| 10 | 210 | 5879 | 6089 | 3.665921 | Randall L. Rathbun | 1998 |
| 11 | 282 | 13397 | 13679 | 4.114085 | Randall L. Rathbun | 1998 |
| 12 | 372 | 18539 | 18911 | 5.075111 | Randall L. Rathbun | 1998 |
| 13 | 498 | 24419 | 24917 | 6.428788 | Randall L. Rathbun | 1998 |
| 14 | 630 | 62297 | 62927 | 6.818872 | Randall L. Rathbun | 1998 |
| 15 | 924 | 187907 | 188831 | 8.269411 | Randall L. Rathbun | 1998 |
| 16 | 930 | 687521 | 688451 | 6.796202 | Randall L. Rathbun | 1998 |
| 17 | 1008 | 688451 | 689459 | 7.364664 | Randall L. Rathbun | 1998 |
| 18 | 1452 | 850349 | 851801 | 10.28279 | Randall L. Rathbun | 1998 |
| 19 | 1512 | 2868959 | 2870471 | 9.028724 | Randall L. Rathbun | 1998 |
| 20 | 1530 | 4869911 | 4871441 | 8.519248 | Randall L. Rathbun | 1998 |
| 21 | 1722 | 9923987 | 9925709 | 8.759769 | Randall L. Rathbun | 1998 |
| 22 | 1902 | 14656517 | 14658419 | 9.223564 | Randall L. Rathbun | 1998 |
| 23 | 2190 | 17382479 | 17384669 | 10.40397 | Randall L. Rathbun | 1998 |
| 24 | 2256 | 30752231 | 30754487 | 10.02002 | Randall L. Rathbun | 1998 |
| 25 | 2832 | 32822369 | 32825201 | 12.48380 | Randall L. Rathbun | 1998 |
| 26 | 2868 | 96894041 | 96896909 | 11.19789 | Randall L. Rathbun | 1998 |
| 27 | 3012 | 136283429 | 136286441 | 11.33568 | Randall L. Rathbun | 1998 |
| 28 | 3102 | 234966929 | 234970031 | 11.02389 | Randall L. Rathbun | 1998 |
| 29 | 3180 | 248641037 | 248644217 | 11.23505 | Randall L. Rathbun | 1998 |
| 30 | 3480 | 255949949 | 255953429 | 12.25819 | Randall L. Rathbun | 1998 |
| 31 | 3804 | 390817727 | 390821531 | 12.83226 | Randall L. Rathbun | 1998 |
| 32 | 4770 | 698542487 | 698547257 | 15.18626 | Randall L. Rathbun | 1998 |
| 33 | 5292 | 2466641069 | 2466646361 | 14.93973 | Randall L. Rathbun | 1998 |
| 34 | 6030 | 4289385521 | 4289391551 | 16.18444 | Randall L. Rathbun | 1998 |
| 35 | 6282 | 19181736269 | 19181742551 | 14.79506 | Randall L. Rathbun | 1998 |
| 36 | 6474 | 24215097497 | 24215103971 | 14.95151 | Randall L. Rathbun | 1998 |
| 37 | 6552 | 24857578817 | 24857585369 | 15.09856 | Randall L. Rathbun | 1998 |
| 38 | 6648 | 40253418059 | 40253424707 | 14.72091 | Randall L. Rathbun | 1998 |
| 39 | 7050 | 42441715487 | 42441722537 | 15.54361 | Randall L. Rathbun | 1998 |
| 40 | 7980 | 43725662621 | 43725670601 | 17.55126 | Randall L. Rathbun | 1998 |
| 41 | 8040 | 65095731749 | 65095739789 | 17.12254 | Randall L. Rathbun | 1998 |
| 42 | 8994 | 134037421667 | 134037430661 | 18.08956 | Marek Wolf | 1999 |
| 43 | 9312 | 198311685749 | 198311695061 | 18.16933 | Marek Wolf | 1999 |
| 44 | 9318 | 223093059731 | 223093069049 | 18.01755 | Marek Wolf | 1999 |
| 45 | 10200 | 353503437239 | 353503447439 | 19.04609 | Marek Wolf | 1999 |
| 46 | 10338 | 484797803249 | 484797813587 | 18.85325 | Marek Wolf | 1999 |
| 47 | 10668 | 638432376191 | 638432386859 | 19.06301 | Marek Wolf | 1999 |
| 48 | 10710 | 784468515221 | 784468525931 | 18.85126 | Marek Wolf | 1999 |
| 49 | 11388 | 794623899269 | 794623910657 | 20.02584 | Marek Wolf | 1999 |
| 50 | 11982 | 1246446371789 | 1246446383771 | 20.39474 | Marek Wolf | 1999 |
| 51 | 12138 | 1344856591289 | 1344856603427 | 20.54799 | Marek Wolf | 1999 |
| 52 | 12288 | 1496875686461 | 1496875698749 | 20.64329 | Marek Wolf | 1999 |
| 53 | 12630 | 2156652267611 | 2156652280241 | 20.67568 | Marek Wolf | 1999 |
| 54 | 13050 | 2435613754109 | 2435613767159 | 21.18140 | Marek Wolf | 1999 |
| 55 | 14262 | 4491437003327 | 4491437017589 | 22.18628 | Marek Wolf | 1999 |
| 56 | 14436 | 13104143169251 | 13104143183687 | 20.89295 | Marek Wolf | 1999 |
| 57 | 14952 | 14437327538267 | 14437327553219 | 21.50158 | Marek Wolf | 1999 |
| 58 | 15396 | 18306891187511 | 18306891202907 | 21.79709 | Richard Fischer | 2008 |
| 59 | 15720 | 18853633225211 | 18853633240931 | 22.21297 | Richard Fischer | 2008 |
| 60 | 16362 | 23275487664899 | 23275487681261 | 22.80468 | Richard Fischer | 2008 |
| 61 | 16422 | 23634280586867 | 23634280603289 | 22.86557 | Richard Fischer | 2008 |
| 62 | 16590 | 38533601831027 | 38533601847617 | 22.38321 | Richard Fischer | 2008 |
| 63 | 16896 | 43697538391391 | 43697538408287 | 22.61387 | Richard Fischer | 2008 |
| 64 | 17082 | 56484333976919 | 56484333994001 | 22.49368 | Richard Fischer | 2008 |
| 65 | 18384 | 74668675816277 | 74668675834661 | 23.78699 | Richard Fischer | 2008 |
| 66 | 19746 | 116741875898981 | 116741875918727 | 24.84912 | Richard Fischer | 2008 |
| 67 | 19992 | 136391104728629 | 136391104748621 | 24.91878 | Richard Fischer | 2008 |
| 68 | 20532 | 221346439666109 | 221346439686641 | 24.84704 | Richard Fischer | 2008 |
| 69 | 21930 | 353971046703347 | 353971046725277 | 25.80021 | Richard Fischer | 2008 |
| 70 | 22548 | 450811253543219 | 450811253565767 | 26.14839 | Richard Fischer | 2008 |
| 71 | 23358 | 742914612256169 | 742914612279527 | 26.30315 | Richard Fischer | 2008 |
| 72 | 23382 | 1121784847637957 | 1121784847661339 | 25.70768 | Richard Fischer | 2008 |
| 73 | 25230 | 1149418981410179 | 1149418981435409 | 27.70057 | Richard Fischer | 2008 |
| 74 | 26268 | 2543288406389231 | 2543288406415499 | 27.56324 | Tomás Oliveira e Silva | 2013 |
| 75 | 28842 | 2797282815481499 | 2797282815510341 | 30.10238 | Tomás Oliveira e Silva | 2013 |
| 76 | 31302 | 12914226879316517 | 12914226879347819 | 30.03118 | Robert Smith | 2019 |
| 77 | 31482 | 16155559543324757 | 16155559543356239 | 29.84250 | Thomas Ritschel | 2019 |
| 78 | 31512 | 37338553629118097 | 37338553629149609 | 28.57373 | Martin Raab | 2019 |
| 79 | 31920 | 37962553054417547 | 37962553054449467 | 28.91856 | Martin Raab | 2019 |
| 80 | 33042 | 38617975949216087 | 38617975949249129 | 29.90823 | Martin Raab | 2019 |
| 81 | 34692 | 52000545890760149 | 52000545890794841 | 30.91813 | Martin Raab | 2020 |
| 82 | 35640 | 70478530884377381 | 70478530884413021 | Martin Raab | 2021 | |
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