# Prime Number Records

This page lists my prime number discoveries which held the record for largest prime number in their respective categories at time of discovery.

The last column in each table lists the approximate dates that each number spent as the record holder.

The number in the digits column also contains a link to the number's entry on the Prime Pages.

## Generalized Repunit Primes

A repunit is a number consisting of only the digit '1', like 11 or 11111, in base 10.
A generalized repunit (GRU) is a repunit in another base b, and can be written (bn-1)/(b-1), to represent n ones in base b.
A generalized repunit prime is a generalized repunit number that is prime.

Number (p) Digits Time Spent as Record Holder
(717624691 - 1)/7175 95202 June 2017 - present [1]
(4073416111 - 1)/40733 74267 March 2015 - June 2017
(6384713339 - 1)/63846 64091 May 2013 - March 2015
(2637113681 - 1)/26370 60482 February 2012 - May 2013
(3412011311 - 1)/34119 51269 September 2011 - February 2012
(325569283 - 1)/32555 41887 April 2011 - September 2011
(154912973 - 1)/1548 41382 December 2010 - April 2011
[1] NOTE: (717624691 - 1)/7175 also holds the record for the largest non-trivial gigantic (NTG) prime.

## Sophie Germain Primes

A prime p is a Sophie Germain prime if 2p+1 is prime as well.

Number (p) Digits Time Spent as Record Holder
183027 × 2265440 - 1 79911 March 2010 - April 2012
607095 × 2176311 - 1 53081 September 2009 - November 2009

## Cunningham Chain second kind, length 2

For this type of number, p and 2p-1 must be prime.

Number (p) Digits Time Spent as Record Holder
648309 × 2148310 + 1 44652 July 2010 - July 2014
552903 × 2136156 + 1 40993 June 2010 - July 2010
163221 × 2124600 + 1 37514 December 2009 - June 2010
532323 × 2104389 + 1 31430 November 2009 - December 2009

## Cunningham Chain first kind, length 3

For this type of number, p, 2p+1, and 4p+3 must all be prime.

Number (p) Digits Time Spent as Record Holder
914546877 × 234772 - 1 10477 January 2010 - April 2014
379185609 × 227127 - 1 8175 November 2009 - January 2010

## Cunningham Chain second kind, length 3

For this type of number, p, 2p-1, and 4p-3 must all be prime.

Number (p) Digits Time Spent as Record Holder
82659189 × 226997 + 1 8135 March 2010 - July 2014
173028555 × 226993 + 1 8134 February 2010 - March 2010
55339083 × 219400 + 1 5848 December 2009 - February 2010
387977793 × 217864 + 1 5387 October 2009 - December 2009