| type | pattern | initial Skewes number | n-th | when | discoverer(s) |
| prime | p | unknown | |||
| twin | p, p+2 | 1 369 391 | 10 744 | 14 Jul 2011 | Marek Wolf |
| cousin | p, p+4 | 5 206 837 | 33 480 | 16 Sep 2019 | László Tóth |
| sexy | p, p+6 | unknown | |||
| triplet | p, p+2, p+6 | 87 613 571 | 49 767 | 16 Sep 2019 | László Tóth |
| triplet | p, p+4, p+6 | 337 867 | 652 | 16 Sep 2019 | László Tóth |
| 4-tuplet | p, p+2, p+6, p+8 | 1 172 531 | 202 | 16 Sep 2019 | László Tóth |
| cousin pair | p, p+4, p+6, p+10 | 827 929 093 | 48 909 | 16 Sep 2019 | László Tóth |
| 5-tuplet | p, p+2, p+6, p+8, p+12 | 21 432 401 | 267 | 16 Sep 2019 | László Tóth |
| 5-tuplet | p, p+4, p+6, p+10, p+12 | 216 646 267 | 1208 | 16 Sep 2019 | László Tóth |
| 6-tuplet | p, p+4, p+6, p+10, p+12, p+16 | 251 331 775 687 | 17 581 | 16 Sep 2019 | László Tóth |
| 7-tuplet | p, p+2, p+6, p+8, p+12, p+18, p+20 | 7 572 964 186 421 | 27 136 | 09 May 2020 | Hugo Pförtner |
| 7-tuplet | p, p+2, p+8, p+12, p+14, p+18, p+20 | 214 159 878 489 239 | 348 633 | 11 May 2020 | Hugo Pförtner |
| 8-tuplet | p, p+2, p+6, p+8, p+12, p+18, p+20, p+26 | 1 203 255 673 037 261 | 134 292 | 26 Aug 2021 | Hugo Pförtner; Norman Luhn |
| 8-tuplet | p, p+2, p+6, p+12, p+14, p+20, p+24, p+26 | 523 250 002 674 163 757 | 40 634 356 | 11 Sep 2021 | Norman Luhn; Hugo Pförtner |
| 8-tuplet | p, p+6, p+8, p+14, p+18, p+20, p+24, p+26 | 750 247 439 134 737 983 | 20 316 822 | 26 Aug 2021 | Hugo Pförtner; Norman Luhn |
| 9-tuplet | p, p+2, p+6, p+8, p+12, p+18, p+20, p+26, p+30 | 3 658 988 336 628 289 781 | 6 188 042 | 03 Jun 2026 | Karl Desfontaines; Hugo Pförtner |