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 |