The Chronology of Prime Number Records

Contents:

Largest | Twin | Sophie Germain | Mersenne | Factorial/Primorial | Cullen | Woodall

Comments and Suggestions

The Largest Known Prime Records

(see also the pages: The top 20: largest known primes)

On November 17, 2003, the computer of Michael Shafer, one of the members of the Great Internet Mersenne Prime Search, discovered the new prime record: 2^20996011-1, running George Woltman's program Prime95 connected to Scott Kurowski's Internet PrimeNet Server. 

The Twin Prime Records

(see also the pages: The top 20: twin primes)

Twin primes are primes of the form p and p+2, i.e., they differ by two.

On September 28, 2002, Daniel Papp discovered a 51090 digits twin prime record 33218925.2¹⁶⁹⁶⁹⁰+/-1, with a set of different programs: Paul Jobling's NewPGen, George Woltman's PRP and Yves Gallot's Proth.exe. David Underbakke and Phil Carmody found the previous record, on May 17, 2001.

The Sophie Germain Prime Records

(see also the pages: The top 20: Sophie Germain primes)

A Sophie Germain prime is an odd prime p for which 2p+1 is also a prime.

On January 18, 2003, David Underbakke discovered a 34547digits Sophie Germain prime record 2540041185.2¹¹⁴⁷²⁹-1, with a set of different programs: his own TwinGen, George Woltman's PRP and Yves Gallot's Proth.exe. Michael Angel, Dirk Augustin and Paul Jobling found the previous record on November 18, 2002.

The Mersenne Prime Records

(see also the pages: The top 20: Mersenne primes)

Mersenne primes are of the form 2^p-1

On November 17, 2003, the computer of Michael Shafer, one of the members of the Great Internet Mersenne Prime Search, found the 40^th known Mersenne prime: 2^20996011-1, running George Woltman's program Prime95 connected to Scott Kurowski's Internet PrimeNet Server.  

The Factorial/Primorial Prime Records

(see also the pages: The top 20: factorial/primorial primes)

Numbers of the form n!+/-1 are called factorial primes.

Primorial Primes are of the form 2.3.5.p +1.

The Cullen Prime Records

(see also the pages: The top 20: Cullen primes)

The Cullen Primes are of the form n 2ⁿ + 1.

On September 30, 1998, Masakatu Morii discovered a 145072 digits Cullen prime record with Yves Gallot's Proth.exe : 481899.2⁴⁸¹⁸⁹⁹+1. Darren Smith found the previous record, also using the same program, on July 31, 1998.

The Woodall Prime Records

(see also the pages: The top 20: Woodall primes)

The Woodall Primes are of the form n 2ⁿ - 1.

On September 25, 2000, Manfred Toplic discovered a 200815 digits Woodall prime record with Yves Gallot's Proth.exe : 667071.2⁶⁶⁷⁰⁷¹-1. Kevin O'Hare found the previous record, also using the same program, on May 1, 1998.

Comments and Suggestions

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Page by Lucile and Yves Gallot <galloty@wanadoo.fr>

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