My Proven Prime Records

FactoProth
Largest known of the following types

Twin
23! ^. 2⁶⁸⁶⁸±1    (2090 digits)

Sophie Germain
86! ^. 2⁷⁸⁶⁴-1    (2498 digits)
86! ^. 2⁷⁸⁶⁵-1    (2498 digits)

Cunningham Chain of the second kind (Length = 2)
1011! ^. 2⁶⁰⁴+1    (2783 digits)
1011! ^. 2⁶⁰⁵+1    (2783 digits)

PrimoProth
Largest known of the following types

Twin
11197# ^. 2¹⁰¹⁸²±1    (7875 digits)

Sophie Germain
8753# ^. 2⁷⁸⁰²-1    (6103 digits)
8753# ^. 2⁷⁸⁰³-1    (6103 digits)

Cunningham Chain of the second kind (Length = 2)
6553# ^. 2¹⁶⁷²⁷+1    (7838 digits)
6553# ^. 2¹⁶⁷²⁸+1    (7839 digits)

Cunningham Chain of the first kind (Length = 3)
383# ^. 2¹⁰²-1    (187 digits)
383# ^. 2¹⁰³-1    (187 digits)
383# ^. 2¹⁰⁴-1    (188 digits)

All prime numbers on this page were found by me and are listed on Henri Lifchitz's FactoProth and PrimoProth Records page. All prime numbers on this page were proven prime with Pocklington's N-1 test or Morrison's N+1 test in the PrimeForm (OpenPFGW) program.

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Last updated on February 24, 2006
Donovan Johnson