| k | Smallest 4 bit prime k-tuplets |
| 1 | 23 + 3 |
| 2 | 23 + 3 + d, d = 0, 2 |
| k | Smallest 8 bit prime k-tuplets |
| 1 | 27 + 3 |
| 2 | 27 + 9 + d, d = 0, 2 |
| 3 |
27 + 63 + d, d = 0, 2, 6 27 + 65 + d, d = 0, 4, 6 |
| 4 | 27 + 63 + d, d = 0, 2, 6, 8 |
| k | Smallest 16 bit prime k-tuplets |
| 1 | 215 + 3 |
| 2 | 215 + 33 + d, d = 0, 2 |
| 3 |
215 + 579 + d, d = 0, 2, 6 215 + 29 + d, d = 0, 4, 6 |
| 4 | 215 + 2073 + d, d = 0, 2, 6, 8 |
| 5 |
215 + 11013 + d, d = 0, 2, 6, 8, 12 215 + 11009 + d, d = 0, 4, 6, 10, 12 |
| 6 | 215 + 11009 + d, d = 0, 4, 6, 10, 12, 16 |
| k | Smallest 32 bit prime k-tuplets |
| 1 | 231 + 11 |
| 2 | 231 + 219 + d, d = 0, 2 |
| 3 |
231 + 963 + d, d = 0, 2, 6 231 + 389 + d, d = 0, 4, 6 |
| 4 | 231 + 86913 + d, d = 0, 2, 6, 8 |
| 5 |
231 + 273603 + d, d = 0, 2, 6, 8, 12 231 + 1162739 + d, d = 0, 4, 6, 10, 12 |
| 6 | 231 + 3139049 + d, d = 0, 4, 6, 10, 12, 16 |
| 7 |
231 + 18611763 + d, d = 0, 2, 6, 8, 12, 18, 20 231 + 14251911 + d, d = 0, 2, 8, 12, 14, 18, 20 |
| 8 |
231 + 249953853 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 231 + 101879445 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 231 + 143216889 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 |
| 9 |
231 + 695864703 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 231 + 187732325 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 231 + 818519409 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 231 + 410727911 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
| k | Smallest 64 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 263 + 29 | - | - | Prime |
| 2 | 263 + 1533 + d, d = 0, 2 | - | - | Prime |
| 3 |
263 + 8223 + d, d = 0, 2, 6 263 + 39035 + d, d = 0, 4, 6 |
- | - | Prime |
| 4 | 263 + 1980513 + d, d = 0, 2, 6, 8 | - | - | Prime |
| 5 |
263 + 14486103 + d, d = 0, 2, 6, 8, 12 263 + 4757729 + d, d = 0, 4, 6, 10, 12 |
- | - | Prime |
| 6 | 263 + 426501059 + d, d = 0, 4, 6, 10, 12, 16 | - | - | Prime |
| 7 |
263 + 4705604193 + d, d = 0, 2, 6, 8, 12, 18, 20 263 + 2966310861 + d, d = 0, 2, 8, 12, 14, 18, 20 |
- | - | Prime |
| 8 |
263 + 4705604193 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 263 + 17012119749 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 263 + 110756143005 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 |
Norman Luhn | 26 Jul 2023 | Prime |
| 9 |
263 + 452820907143 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 263 + 168519506135 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 263 + 100532048769 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 263 + 3378108971741 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
Norman Luhn | 26 Jul 2023 | Prime |
| 10 |
263 + 1348558119513 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 263 + 12757330800639 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 |
Norman Luhn | - | Prime |
| 11 |
263 + 466426651365783 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 263 + 121272982354595 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36 |
Norman Luhn | - | Prime |
| 12 |
263 + 3470522132102133 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 263 + 121272982354589 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 |
Norman Luhn | - | Prime |
| 13 |
263 + 25594754679129513 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 263 + 30994641618675845 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 263 + 60293901012505385 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 263 + 19038040876189161 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 263 + 42091525840764111 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 263 + 62249596355431313 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 |
Norman Luhn | - | Prime |
| 14 |
263 + 3647164112776879803 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 263 + 1533046308220071471 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 |
Vladimir Vlesycit Tony Forbes |
2006 1997 |
Prime |
| 15 |
263 + 4870678833257091675 + d, d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 263 + 8681787723510471579 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 263 + 198766083312189039 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 |
Jens Kruse Andersen Jim Morton Jörg Waldvogel |
2007 2001 2009 |
Prime |
| k | Smallest 128 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 2127 + 29 | - | - | Prime |
| 2 | 2127 + 993 + d, d = 0, 2 | - | - | Prime |
| 3 |
2127 + 385683 + d, d = 0, 2, 6 2127 + 332819 + d, d = 0, 4, 6 |
- | - | Prime |
| 4 | 2127 + 6061533 + d, d = 0, 2, 6, 8 | - | - | Prime |
| 5 |
2127 + 110549973 + d, d = 0, 2, 6, 8, 12 2127 + 1458962369 + d, d = 0, 4, 6, 10, 12 |
- | - | Prime |
| 6 | 2127 + 28041748319 + d, d = 0, 4, 6, 10, 12, 16 | - | - | Prime |
| 7 |
2127 + 746574171513 + d, d = 0, 2, 6, 8, 12, 18, 20 2127 + 272313886581 + d, d = 0, 2, 8, 12, 14, 18, 20 | Norman Luhn | 08 Aug 2023 | Prime |
| 8 |
2127 + 63715848976383 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 2127 + 80754868149 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 2127 + 27046297675785 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 |
Norman Luhn | 08 Aug 2023 | Prime |
| 9 |
2127 + 1442323732982463 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 2127 + 480574331083595 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 2127 + 25194649717269 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 2127 + 143592769997711 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
Norman Luhn | 12 Aug 2023 | Prime |
| 10 |
2127 + 16918106943693363 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 2127 + 17354524326013599 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 |
Norman Luhn | 14 Aug 2023 | Prime |
| 11 |
2127 + 872606664012499173 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 2127 + 17354524326013595 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36 |
Norman Luhn | 14 Aug 2023 | Prime |
| 12 |
2127 + 39897556794426346773 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 2127 + 50402190017439454139 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 |
Norman Luhn | 16 Aug 2023 18 Aug 2023 |
Prime |
| 13 |
2127 + 63350233650289470873 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 2127 + 1242071648883580401695 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 2127 + 424748909503662333695 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 2127 + 514413217431519739221 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 2127 + 2320764486629670280791 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 2127 + 633485696659138527143 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 |
Norman Luhn | 29 Nov 2023 01 Dec 2023 22 Dec 2023 24 Dec 2023 28 Dec 2023 29 Dec 2023 |
Prime |
| k | Smallest 256 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 2255 + 95 | - | - | Prime |
| 2 | 2255 + 1269 + d, d = 0, 2 | - | - | Prime |
| 3 |
2255 + 635433 + d, d = 0, 2, 6 2255 + 1029635 + d, d = 0, 4, 6 |
- | - | Prime |
| 4 | 2255 + 313528833 + d, d = 0, 2, 6, 8 | - | - | Prime |
| 5 |
2255 + 37103954583 + d, d = 0, 2, 6, 8, 12 2255 + 14355087569 + d, d = 0, 4, 6, 10, 12 |
- | - | Prime |
| 6 | 2255 + 2899462948079 + d, d = 0, 4, 6, 10, 12, 16 | Norman Luhn | 26 Jul 2023 | Prime |
| 7 |
2255 + 313197125029533 + d, d = 0, 2, 6, 8, 12, 18, 20 2255 + 162164467658091 + d, d = 0, 2, 8, 12, 14, 18, 20 |
Norman Luhn | 08 Aug 2023 | Prime |
| 8 |
2255 + 694118876535423 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 2255 + 2240899208991249 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 2255 + 8115490943504655 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 |
Norman Luhn | 08 Aug 2023 | Prime |
| 9 |
2255 + 391763851776827253 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 2255 + 170028409287048695 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 2255 + 7501261050075399 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 2255 + 600604066539705851 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
Norman Luhn | 12 Aug 2023 12 Aug 2023 13 Aug 2023 13 Aug 2023 |
Prime |
| 10 |
2255 + 35723838822699340113 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 2255 + 3030735700318485549 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 |
Norman Luhn | 03 Jan 2024 04 Jan 2024 |
Prime |
| k | Smallest 512 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 2511 + 111 | - | - | Prime |
| 2 | 2511 + 76509 + d, d = 0, 2 | - | - | Prime |
| 3 |
2511 + 26393763 + d, d = 0, 2, 6 2511 + 3876659 + d, d = 0, 4, 6 |
- | - | Prime |
| 4 | 2511 + 5719942173 + d, d = 0, 2, 6, 8 | - | - | Prime |
| 5 |
2511 + 1094261901693 + d, d = 0, 2, 6, 8, 12 2511 + 692441651759 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn | 07 Aug 2023 | Prime |
| 6 | 2511 + 191360651339309 + d, d = 0, 4, 6, 10, 12, 16 | Norman Luhn | 08 Aug 2023 | Prime |
| 7 |
2511 + 25779040088876223 + d, d = 0, 2, 6, 8, 12, 18, 20 2511 + 3722157409293381 + d, d = 0, 2, 8, 12, 14, 18, 20 |
Norman Luhn | 11 Aug 2023 | Prime |
| 8 |
2511 + 210197440919245383 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 2511 + 609595131024077769 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 2511 + 200851397687832825 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 |
Norman Luhn | 18 Feb 2024 21 Feb 2024 22 Feb 2024 |
Prime |
| k | Smallest 1024 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 21023 + 1155 | - | - | Prime |
| 2 | 21023 + 303039 + d, d = 0, 2 | - | - | Prime |
| 3 |
21023 + 43354383 + d, d = 0, 2, 6 21023 + 5073689 + d, d = 0, 4, 6 |
Norman Luhn | 27 Jul 2023 | Prime |
| 4 | 21023 + 60396644163 + d, d = 0, 2, 6, 8 | Norman Luhn | 27 Jul 2023 | Prime |
| 5 |
21023 + 2543929894263 + d, d = 0, 2, 6, 8, 12 21023 + 6133998677609 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn | 07 Aug 2023 | Prime |
| 6 | 21023 + 1846048636007609 + d, d = 0, 4, 6, 10, 12, 16 | Norman Luhn | 27 Aug 2023 | Prime |
| k | Smallest 211 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 22047 + 1919 | - | - | Prime |
| 2 | 22047 + 977181 + d, d = 0, 2 | Anonymous | 19 Jun 2023 | Prime |
| 3 |
22047 + 2642851443 + d, d = 0, 2, 6 22047 + 3218849 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Anonymous ( Primo ) |
27 Jul 2023 | Prime |
| 4 | 22047 + 401791781973 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP ) "A.C." ( proven primes via CM ) |
07 Aug 2023 | Prime |
| 5 |
22047 + 591994566506673 + d, d = 0, 2, 6, 8, 12 22047 + 272317418881889 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn ( PRP / proven primes via Primo ) | 25 Aug 2023 26 Aug 2023 |
Prime |
| k | Smallest 212 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 24095 + 579 | Edwin Hall | 02 Dec 2011 | Prime |
| 2 | 24095 + 692349 + d, d = 0, 2 | Norman Luhn ( PRP ) Anonymous ( Primo ) |
27 Jul 2023 | Prime |
| 3 |
24095 + 485145813 + d, d = 0, 2, 6 24095 + 8477058269 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) "A.C." ( proven primes via CM ) |
06 Aug 2023 07 Aug 2023 |
Prime |
| 4 | 24095 + 10193259640923 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP ) "A.C." ( proven primes via CM ) |
07 Aug 2023 | Prime |
| k | Smallest 213 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 28191 + 1911 | Roberts | 07 Dec 2013 | Prime |
| 2 | 28191 + 2441931 + d, d = 0, 2 | Norman Luhn ( PRP ) Maia Karpovich ( proven primes via CM ) |
27 Jul 2023 30 Jul 2023 |
Prime |
| 3 |
28191 + 10618046763 + d, d = 0, 2, 6 28191 + 41352257999 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Anonymous ( proven primes via CM ) |
06-07 Aug 2023 27 Oct 2023 |
Prime |
| k | Smallest 214 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 216383 + 20253 | Norman Luhn ( PRP ) Maia Karpovich ( proven prime via CM ) |
27 Jul 2023 30 Jul 2023 |
Prime |
| 2 | 216383 + 39271251 + d, d = 0, 2 | Norman Luhn ( PRP ) Anonymous ( proven primes via CM ) |
06 Aug 2023 27 Oct 2023 |
Prime |
| 3 |
216383 + 222418926039 + d, d = 0, 2, 6 216383 + 988791230339 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) | 28 Oct 2023 04 Nov 2023 |
PRP PRP |
| k | Smallest 215 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 232767 + 34769 | Norman Luhn ( PRP ) Maia Karpovich ( proven prime via CM ) |
06 Aug 2023 30 Oct 2023 |
Prime |
| 2 | 232767 + 42777573 + d, d = 0, 2 | Norman Luhn ( PRP ) | 06 Aug 2023 | PRP |
| k | Smallest 216 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 265535 + 37355 | Norman Luhn ( PRP ) | 06 Aug 2023 | PRP |