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
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
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
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
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 Dï¿½cio
Luiz Gazzoni Filho. PRP found by Pierre Cami.
Konyagin-Pomerance primality proof by David Broadhurst.
May 2005: 25987968300*[RSA-200]^512-1 and
A distributed search for a prime of the form
k*[RSA-200]^512-1 which can only be proven prime by using
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, Gï¿½ran 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.
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
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.