Smallest existing proven prime k-tuplets with 1,000 digits
k Prime k-tuplet Who When
Certificates
1 10999 + 7 - -
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2 10999 + 1975081 + d, d = 0, 2 Daniel Heuer 11 Oct 1999
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3 10999 + 5537073001 + d, d = 0, 2, 6
10999 + 1598241813 + d, d = 0, 4, 6
Norman Luhn -
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4 10999 + 4114571944591 + d, d = 0, 2, 6, 8 Norman Luhn 16 Oct 2004
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5 10999 + 3554007760224751 + d, d = 0, 2, 6, 8, 12
10999 + 3818999670116007 + d, d = 0, 4, 6, 10, 12
Norman Luhn 01 Jun 2014
27 Dec 2019
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Smallest existing proven prime k-tuplets with 2,000 digits
k Prime k-tuplet Who When
Certificates
1 101999 + 7321 Peter Kaiser 25 Jun 2013
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2 101999 + 89316289 + d, d = 0, 2 Norman Luhn 22 May 2021
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3 101999 + 27107552191 + d, d = 0, 2, 6
101999 + 38866053453 + d, d = 0, 4, 6
Norman Luhn 22 May 2021
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4 101999 + 205076414983951 + d, d = 0, 2, 6, 8 Gerd Lamprecht 24 Oct 2017
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Smallest existing proven prime k-tuplets with 3,000 digits
k Prime k-tuplet Who When
Certificates
1 102999 + 1887 Youcef L 2012
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2 102999 + 18893101 + d, d = 0, 2 Masaki UKAI 2020
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3 102999 + 25740029131 + d, d = 0, 2, 6
102999 + 37274603937 + d, d = 0, 4, 6
Norman Luhn 2021
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4 102999 + 339930644528851 + d, d = 0, 2, 6, 8 Norman Luhn 04 May 2022
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Smallest existing proven prime k-tuplets with 4,000 digits
k Prime k-tuplet Who When
Certificates
1 103999 + 4771 Giovanni & Marco La Barbera 2001
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2 103999 + 153668401 + d, d = 0, 2 Norman Luhn 2021
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3 103999 + 182402621497 + d, d = 0, 2, 6
103999 + 243095638113 + d, d = 0, 4, 6
Norman Luhn 2021
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Smallest existing proven prime k-tuplets with 5,000 digits
k Prime k-tuplet Who When
Certificates
1 104999 + 22669 Alexander Mkrtychyan 12 Aug 2013
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2 104999 + 45171901 + d, d = 0, 2 Norman Luhn 2021
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3 104999 + 70852892827 + d, d = 0, 2, 6
104999 + 244793127627 + d, d = 0, 4, 6
Norman Luhn 2021
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Smallest existing proven prime k-tuplets with 6,000 digits
k Prime k-tuplet Who When
Certificates
1 105999 + 29379 Geoffrey Yeung 2020
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2 105999 + 242051191 + d, d = 0, 2 Norman Luhn 2021
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3 105999 + 835812013681 + d, d = 0, 2, 6
105999 + 634115091747 + d, d = 0, 4, 6
Norman Luhn & Oliver Kruse 25 Mar 2022
30 Mar 2022
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Smallest existing proven prime k-tuplets with 7,000 digits
k Prime k-tuplet Who When
Certificates
1 106999 + 33187 Norman Luhn 26 May 2021
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2 106999 + 151203769 + d, d = 0, 2 Norman Luhn & Robert Gelhar 1 Jun 2021
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Smallest existing proven prime k-tuplets with 8,000 digits
k Prime k-tuplet Who When
Certificates
1 107999 + 35887 Norman Luhn & Robert Gelhar 1 Jun 2021
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2 107999 + 439617139 + d, d = 0, 2 Norman Luhn & Robert Gelhar 1 Jun 2021
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Smallest existing proven prime k-tuplets with 9,000 digits
k Prime k-tuplet Who When
Certificates
1 108999 + 3541 Norman Luhn & Robert Gelhar May 2021
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2 108999 + 13215871 + d, d = 0, 2 Norman Luhn & Robert Gelhar May 2021
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Smallest existing proven prime k-tuplets with 10,000 digits
k Prime k-tuplet Who When
Certificates
1 109999 + 33603 Jens Franke, Thorsten Kleinjung & Tobias Wirth 19 Aug 2003
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2 109999 + 2421018649 + d, d = 0, 2 Dirk Augustin & Norman Luhn 2010/2021
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