| k | Smallest 10,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 29999 + 5895 | Ray Chandler ( proven prime via PRIMO ) | 15 Feb 2022 | |
| 2 | 29999 + 79968999 + d, d = 0, 2 | Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
04 Jul 2023 | |
| 3 |
29999 + 50223215439 + d, d = 0, 2, 6 29999 + 39510626279 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
07 Jul 2023 | |
| 4 | 29999 + 244164046679793 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP ) Maia Karpovich ( proven primes via CM ) |
23 Oct 2023 26 Oct 2023 |
| k | Smallest 20,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 219999 + 3191 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
06 Jul 2023 | |
| 2 | 219999 + 168863241 + d, d = 0, 2 | Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
08 Jul 2023 | |
| 3 |
219999 + 5127869884053 + d, d = 0, 2, 6 219999 + 368935649075 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) | 09 Feb 2024 12 Feb 2024 |
PRP |
| k | Smallest 30,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 229999 + 28911 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
04 Jul 2023 | |
| 2 | 229999 + 322389429 + d, d = 0, 2 | Norman Luhn ( PRP ) Frank Doornink ( proven primes via CM ) |
28 Aug 2023 13 Oct 2023 |
| k | Smallest 40,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 239999 + 18065 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
12 Jul 2023 | |
| 2 | 239999 + 1411862541 + d, d = 0, 2 | Norman Luhn ( PRP ) Frank Doornink ( proven primes via CM ) |
31 Aug 2023 23 Oct 2023 |
| k | Smallest 50,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 249999 + 24783 | Norman Luhn ( PRP ) Maia Karpovich ( proven prime via CM ) |
07 Jul 2023 20 Jul 2023 |
|
| 2 | 249999 + 446958861 + d, d = 0, 2 | Norman Luhn ( PRP ) |
06 Nov 2023 | PRP |
| k | Smallest 60,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 259999 + 26453 | Norman Luhn ( PRP ) Frank Doornink ( proven prime via CM ) |
07 Jul 2023 20 Oct 2023 |
|
| 2 | 259999 + 1485868971 + d, d = 0, 2 | Norman Luhn ( PRP ) | 10 Nov 2023 | PRP |
| k | Smallest 70,000 bit prime k-tuplets | Who ? | When ? | Certificates |
| 1 | 269999 + 35583 | Norman Luhn ( PRP ) Frank Doornink ( proven prime via CM ) |
07 Jul 2023 06 Aug 2023 |
Prime |
| 2 | 269999 + 9513029823 + d, d = 0, 2 | Norman Luhn ( PRP ) | 21 Dec 2023 | PRP |
| k | Smallest 80,000 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 279999 + 70589 | Norman Luhn ( PRP ) | 07 Jul 2023 | PRP |
| k | Smallest 90,000 bit prime k-tuplets | Who ? | When ? | Status ? |
| 1 | 289999 + 78761 | Norman Luhn ( PRP ) | 07 Jul 2023 | PRP |