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k Smallest 1,000 digit prime k-tuplets Who When Certificates
1 10999 + 7 First proof by Preda Mihailescu 04 Jan 1998
Prime
2 10999 + 1975081 + d, d = 0, 2 Daniel Heuer 11 Oct 1999
Prime
3 10999 + 5537073001 + d, d = 0, 2, 6
10999 + 1598241813 + d, d = 0, 4, 6 		Norman Luhn
( PRP / proven primes via Primo )		 -
Prime
4 10999 + 4114571944591 + d, d = 0, 2, 6, 8 Norman Luhn
( PRP / proven primes via Primo )		 16 Oct 2004
Prime
5 10999 + 3554007760224751 + d, d = 0, 2, 6, 8, 12
10999 + 3818999670116007 + d, d = 0, 4, 6, 10, 12 		Norman Luhn
( PRP / proven primes via Primo )		 01 Jun 2014
27 Dec 2019
Prime

k Smallest 2,000 digit prime k-tuplets Who When Certificates
1 101999 + 7321 Peter Kaiser ( proven prime via Primo ) 25 Jun 2013
Prime
2 101999 + 89316289 + d, d = 0, 2 Norman Luhn
( PRP / proven primes via Primo )		 22 May 2021
Prime
3 101999 + 27107552191 + d, d = 0, 2, 6
101999 + 38866053453 + d, d = 0, 4, 6 		Norman Luhn
( PRP / proven primes via Primo )		 22 May 2021
Prime
4 101999 + 205076414983951 + d, d = 0, 2, 6, 8 Gerd Lamprecht ( PRP )
Norman Luhn ( proven primes via Primo )		 24 Oct 2017
Prime

k Smallest 3,000 digit prime k-tuplets Who When Certificates
1 102999 + 1887 Youcef L 03 Apr 2012
Prime
2 102999 + 18893101 + d, d = 0, 2 Masaki UKAI 11 Aug 2020
Prime
3 102999 + 25740029131 + d, d = 0, 2, 6
102999 + 37274603937 + d, d = 0, 4, 6 		Norman Luhn
( PRP / proven primes via Primo )		 22 May 2021
Prime
4 102999 + 339930644528851 + d, d = 0, 2, 6, 8 Norman Luhn
( PRP / proven primes via Primo )		 04 May 2022
Prime

k Smallest 4,000 digit prime k-tuplets Who When Certificates
1 103999 + 4771 Giovanni & Marco La Barbera
( proven prime via Primo )		 May 2001
Prime
2 103999 + 153668401 + d, d = 0, 2 Norman Luhn
( PRP / proven primes via Primo )		 22 May 2021
Prime
3 103999 + 182402621497 + d, d = 0, 2, 6
103999 + 243095638113 + d, d = 0, 4, 6 		Norman Luhn
( PRP / proven primes via Primo )		 23 May 2021
Prime

k Smallest 5,000 digit prime k-tuplets Who When Certificates
1 104999 + 22669 Alexander Mkrtychyan
( proven prime via Primo )		 12 Aug 2013
Prime
2 104999 + 45171901 + d, d = 0, 2 Norman Luhn
( PRP / proven primes via Primo )		 23 May 2021
Prime
3 104999 + 70852892827 + d, d = 0, 2, 6
104999 + 244793127627 + d, d = 0, 4, 6 		Norman Luhn
( PRP / proven primes via Primo )		 28 May 2021
Prime

k Smallest 6,000 digit prime k-tuplets Who When Certificates
1 105999 + 29379 Geoffrey Yeung
( proven prime via Primo )		 04 Jan 2020
Prime
2 105999 + 242051191 + d, d = 0, 2 Norman Luhn
( PRP / proven primes via Primo )		 25 May 2021
Prime
3 105999 + 835812013681 + d, d = 0, 2, 6
105999 + 634115091747 + d, d = 0, 4, 6 		Norman Luhn ( PRP )
Oliver Kruse ( proven primes via Primo )		 25 Mar 2022
30 Mar 2022
Prime

k Smallest 7,000 digit prime k-tuplets Who When Certificates
1 106999 + 33187 Norman Luhn
( PRP / proven prime via Primo )		 26 May 2021
Prime
2 106999 + 151203769 + d, d = 0, 2 Norman Luhn ( PRP )
Robert Gelhar ( proven primes via Primo )		 01 Jun 2021
Prime
3 106999 + 1141791245437 + d, d = 0, 2, 6
106999 + 1868862621087 + d, d = 0, 4, 6 		Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM )		 16 Aug 2022
14 Sep 2022
Prime

k Smallest 8,000 digit prime k-tuplets Who When Certificates
1 107999 + 35887 Norman Luhn ( PRP )
Robert Gelhar ( proven prime via Primo )		 01 Jun 2021
Prime
2 107999 + 439617139 + d, d = 0, 2 Norman Luhn ( PRP )
Robert Gelhar ( proven primes via Primo )		 01 Jun 2021
Prime
3 107999 + 1600488488131 + d, d = 0, 2, 6
107999 + 59692204797 + d, d = 0, 4, 6 		Norman Luhn ( PRP )
Oliver Kruse ( proven prime via CM )		 05 / 07 Jun 2023
04 Jul 2023
Prime

k Smallest 9,000 digit prime k-tuplets Who When Certificates
1 108999 + 3541 Norman Luhn ( PRP )
Robert Gelhar ( proven prime via Primo )		 01 Jun 2021
Prime
2 108999 + 13215871 + d, d = 0, 2 Norman Luhn ( PRP )
Robert Gelhar ( proven primes via Primo )		 01 Jun 2021
Prime