Primeform e-group


A titan, as defined by Samuel Yates, is anyone who has found a titanic prime. This page provides data on those that have found these primes. The data below only reflects on the primes currently on the list. (Many of the terms that are used here are explained on another page.)

Proof-code(s): p62, p159, p174, x9, x15, x19, p180, p308, p406
E-mail address: (e-mail address unpublished)
Web page:
Username egroup (entry created on 10/27/2001 18:22:52 UTC)
Database id:339 (entry last modified on 5/11/2021 03:36:34 UTC)
Active primes:on current list: 11, rank by number 10
Total primes: number ever on any list: 6005
Production score: for current list 29 (normalized: 0), total 41.4804, rank by score 23
Largest prime: "41769334305470218025...(102088 other digits)...13913798335329393079" ‏(‎102128 digits) via code p62 on 5/26/2005 20:23:54 UTC
Most recent: 51456836560 · 5303# + 1 ‏(‎2271 digits) via code p406 on 8/19/2019 13:51:55 UTC
Entrance Rank: mean 96724.36 (minimum 92044, maximum 103514)

Descriptive Data: (report abuse)

August 2017 - August 2019: AP8 search
We examined k*5303#+1, k in [50000000000, 98000000000]. One Opteron GHz year sieving with NewPGen. 185 Opteron GHz years PRP with bespoke GWNUM program by Paul Underwood resulting in 140,440,486 PRPs. These were searched and extended with Norman Luhn's program on a two 8 core AMD Ryzen 1700 over 420 GHz days. One AP8 was found and 446 AP7s. Ken Davis found 6 CC4s with the PRP data set.

November 2010 - April 2013: AP9 search
We examined k*2371#+1, k in [50000000000, 94000000000]. After 1GHz year sieving with NewPGen, to a depth of 8.5 trillion, we had 11,514,338,127 candidates. These were PRP'd with pfgw64 for 35 GHz years to leave 261,601,878 3-PRP's. With a further 82.5 GHz years, we detected the first 5 known titanic AP9s: 1, 2, 3, 4, 5. A CC5 of the 2nd kind byproduct was also found. Thanks to Mike Oakes and Ken Davis for their wetware before major computations were undertaken by Ken Davis and Paul Underwood.

October 2005: (1284991359*2^98305+1)*(96060285*2^135170+1)-2
Largest known Chen prime. BLS provable form and preparations by Jens Kruse Andersen. Trial factoring program to 2^31 by Phil Carmody. PrimeForm PRP tests by Jens Kruse Andersen, Pierre Cami, Jason Earls, Micha Fleuren, Andy Klingeleers, Paul Underwood, Thomas Wolter. Prp found by Micha Fleuren. Brillhart-Lehmer-Selfridge proof with 42% N+1 factorization by PrimeForm.

July 2005: Two 100,000 digit "Picture Primes".
Writing them 50 digits per line forms a text. Picture design by Paul Underwood. Primo primality proofs of N+1 factors and sieving to 10^12 by Jens Kruse Andersen. PrimeForm prp tests by Jens Kruse Andersen, James Chislett, Jason Earls, V. M. Ulyanov, Paul Underwood, Thomas Wolter. Prps found by Jason Earls and Thomas Wolter. Konyagin-Pomerance primality proofs by David Broadhurst.

June 2005: 32476090*C(1531785651*2^10110+18,23)-1
Distributed search for a provable prime of the form p = k*C(x,23)-1 where C is the binomial function. Factoring p+1 to 30.9% and sieving by Jens Kruse Andersen. Proving p+1 factors with Primo by Pierre Cami, Luigi Morelli and V. M. Ulyanov. PRP tests with PrimeForm by the 4 mentioned and D�cio Luiz Gazzoni Filho. PRP found by Pierre Cami. Konyagin-Pomerance primality proof by David Broadhurst.

May 2005: 25987968300*[RSA-200]^512-1 and 49334180280*[RSA-200]^512-1
A distributed search for a prime of the form k*[RSA-200]^512-1 which can only be proven prime by using the factorization of RSA-200, the product of 2 random 100-digit primes. Writing and running sieve to 10^12 by Jens Kruse Andersen. PRP tests by Jens Kruse Andersen, G�ran Axelsson, Pierre Cami, Phil Carmody, Chuck Lasher, Predrag Minovic, Luigi Morelli, Martin Speirs, V. M. Ulyanov, Paul Underwood and Cedric Vonck. Finding and proving primes by Luigi Morelli and Paul Underwood.

January 2005: 22055611200*(10^999+203959)#/(10^999)#-1
A distributed search for a prime on the form p = k*(10^999+203959)#/(10^999)#-1, where the 101 smallest titanic primes divide p+1. Proving p+1 factors, writing and running sieve to 10^12 by Jens Kruse Andersen. PRP tests by David Broadhurst, Pierre Cami, Phil Carmody, Ken Davis, Predrag Minovic, Luigi Morelli and Paul Underwood. Finding and proving prime by David Broadhurst

Years 2001-2002: 10100000-1061403-1
A coordinated team effort of PrimeForm e-group members to search exhaustively for a one hundred thousand digit primes of the form 10^100000-10^k-1 where k is between 33333 and 99999. Trial division sieving program and running of it to 4 billion by Michael Bell. PRP tests by Fermat's Method by 8-legs, James Berwick, Didier Boivin, Michael Bell, Phil Kenny, Wade McBeth, MyJoy18 and Paul Underwood. Brillhart-Lehmer-Selfridge proof using PFGW by Paul Underwood.

Surname: PrimeForm_egroup (used for alphabetizing and in codes).
Unverified primes are omitted from counts and lists until verification completed.
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