k | Smallest 1,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 2999 + 1239 | Andrey Kulsha | - | Prime |
2 | 2999 + 131493 + d, d = 0, 2 | Norman Luhn ( PRP / proven primes via PRIMO ) | 30 Jun 2023 | Prime |
3 |
2999 + 208538079 + d, d = 0, 2, 6 2999 + 81608945 + d, d = 0, 4, 6 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 30 Jun 2023 | Prime |
4 | 2999 + 33899096913 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP / proven primes via PRIMO ) | - | Prime |
5 |
2999 + 4493853079263 + d, d = 0, 2, 6, 8, 12 2999 + 6405588072959 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 30 Jun 2023 | Prime |
6 | 2999 + 12373034057705669 + d, d = 0, 4, 6, 10, 12, 16 | Norman Luhn ( PRP / proven primes via PRIMO ) | 03 Jul 2023 | Prime |
k | Smallest 2,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 21999 + 345 | Markus Tervooren ( PRP / proven prime via PRIMO ) | 16 Mar 2011 | Prime |
2 | 21999 + 1458003 + d, d = 0, 2 | Norman Luhn ( PRP / proven primes via PRIMO ) | 01 Jul 2023 | Prime |
3 |
21999 + 354804993 + d, d = 0, 2, 6 21999 + 1376585669 + d, d = 0, 4, 6 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 01 Jul 2023 | Prime |
4 | 21999 + 253096198293 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP / proven primes via PRIMO ) | 02 Jul 2023 | Prime |
5 |
21999 + 665602680629223 + d, d = 0, 2, 6, 8, 12 21999 + 441836597465189 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 20 Jul 2023 21 Jul 2023 |
Prime |
k | Smallest 3,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 22999 + 233 | Markus Tervooren ( PRP / proven prime via PRIMO ) | 16 Aug 2011 | Prime |
2 | 22999 + 1792551 + d, d = 0, 2 | Norman Luhn ( PRP / proven primes via PRIMO ) | 02 Jul 2023 | Prime |
3 |
22999 + 2668257093 + d, d = 0, 2, 6 22999 + 6711551075 + d, d = 0, 4, 6 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 03 Jul 2023 | Prime |
4 | 22999 + 9156209246163 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO ) |
04 Jul 2023 | Prime |
5 |
22999 + 6424729478696073 + d, d = 0, 2, 6, 8, 12 22999 + 7418461178845439 + d, d = 0, 4, 6, 10, 12 |
Norman Luhn ( PRP / proven primes via PRIMO ) | 05 Aug 2023 24 Aug 2023 |
Prime |
k | Smallest 4,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 23999 + 311 | Markus Tervooren ( PRP / proven prime via PRIMO ) | 02 Oct 2011 | Prime |
2 | 23999 + 3687783 + d, d = 0, 2 | Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO ) |
03 Jul 2023 | Prime |
3 |
23999 + 978673449 + d, d = 0, 2, 6 23999 + 2996980565 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO ) |
03 Jul 2023 | Prime |
4 | 23999 + 7227471561213 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP / proven primes via PRIMO ) | 08 Jul 2023 | Prime |
k | Smallest 5,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 24999 + 3843 | "Greg" ( proven prime via GP/PARI ) | 16 May 2022 | Prime |
2 | 24999 + 2821251 + d, d = 0, 2 | Norman Luhn ( PRP / proven primes via PRIMO ) | 03 Jul 2023 | Prime |
3 |
24999 + 11704701423 + d, d = 0, 2, 6 24999 + 13209000695 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Richard G. ( proven primes via GP/PARI ) Anonymous ( proven primes via PRIMO ) |
03 Jul 2023 | Prime |
4 | 24999 + 211512469851123 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP / proven primes via PRIMO ) | 17 Jul 2023 | Prime |
k | Smallest 6,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 25999 + 4475 | Norman Luhn ( PRP / proven prime via PRIMO ) | 03 Jul 2023 | Prime |
2 | 25999 + 28573281 + d, d = 0, 2 | Norman Luhn ( PRP / proven primes via PRIMO ) | 03 Jul 2023 | Prime |
3 |
25999 + 2473125783 + d, d = 0, 2, 6 25999 + 27748448735 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Richard G. ( proven primes via GP/PARI ) Oliver Kruse ( proven primes via CM ) |
03 Jul 2023 | Prime |
4 | 25999 + 87059009309433 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP / proven primes via PRIMO ) | 22 Sep 2023 | Prime |
k | Smallest 7,000 bit prime k-tuplets | Who ? | When ? | Status ? |
1 | 26999 + 585 | Edwin Hall ( PRP / proven prime via PRIMO ) | 05 Mar 2012 | Prime |
2 | 26999 + 12440451 + d, d = 0, 2 | Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO ) |
04 Jul 2023 | Prime |
3 |
26999 + 3253968573 + d, d = 0, 2, 6 26999 + 16729556939 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) Anonymous ( proven primes via PRIMO ) |
05 Jul 2023 | Prime |
4 |
26999 + 99002425776003 + d, d = 0, 2, 6, 8 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
28 Sep 2023 | Prime |
k | Smallest 8,000 bit prime k-tuplets | Who ? | When ? | Certificates |
1 | 27999 + 2463 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
04 Jul 2023 | |
2 | 27999 + 21178023 + d, d = 0, 2 | Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
04 Jul 2023 | |
3 |
27999 + 75634774749 + d, d = 0, 2, 6 27999 + 47217614525 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
06 Jul 2023 |
k | Smallest 9,000 bit prime k-tuplets | Who ? | When ? | Certificates |
1 | 28999 + 2039 | Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM ) |
04 Jul 2023 | |
2 | 28999 + 5166819 + d, d = 0, 2 | Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
04 Jul 2023 | |
3 |
28999 + 14278135689 + d, d = 0, 2, 6 28999 + 160079214185 + d, d = 0, 4, 6 |
Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) |
07 Jul 2023 |