World Record Factorial Prime Found

rogue · 2010-10-05, 21:14

From http://www.primegrid.com/forum_thread.php?id=1336:

A remarkable discovery was made yesterday in PrimeGrid's PRPNet. Dmitry Domanov found a World Record Factorial prime.

94550!-1 is prime and is 429,390 digits long. It enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Factorial primes and 155th overall.

This is only the 24th known Factorial prime...the 14th discovery in the last 29 years and the first in almost 8 years. Needless to say, this is a very rare find. It more than triples the size of the previous record of 34790!-1 (142891 digits).

paulunderwood · 2010-10-05, 21:37

Here is a fixed link: http://www.primegrid.com/forum_threa...rap=true#26809

Could this be the biggest prime yet that uses general modular reduction?

It's going to take several hours for The Prime Pages to confirm it's a prime

TimSorbet · 2010-10-05, 22:33

Quote:

Originally Posted by paulunderwood

Could this be the biggest prime yet that uses general modular reduction?

Whether it's the largest or not, it's quite large to not be very specialized. From looking at the top 5000, it looks like it's the largest that's not of the form k*b^n+-1. Does that mean it's the largest without using general modular reduction? A great find, in any case.

Congrats to all involved.

paulunderwood · 2010-10-05, 22:40

Quote:

Originally Posted by Mini-Geek

From looking at the top 5000, it looks like it's the largest that's not of the form k*b^n+-1. Does that mean it's the largest without using general modular reduction?

Without using special modular reduction -- it is general.

axn · 2010-12-20, 18:45

Late to the party, but this and this

ixfd64 · 2010-12-20, 23:51

Quote:

Originally Posted by rogue

This is only the 24th known Factorial prime...the 14th discovery in the last 29 years and the first in almost 8 years.

I hope we won't have to wait that long before GIMPS finds its next prime!

rogue · 2010-12-21, 00:14

Quote:

Originally Posted by ixfd64

I hope we won't have to wait that long before GIMPS finds its next prime!

I doubt GIMPS will. The world record primorial, currently being double-checked, would be the first -1 primorial in 18 years.

rogue · 2012-03-02, 14:38

A new world record primorial has been found by PrimeGrid, http://www.primegrid.com/forum_thread.php?id=4146. It is 476,311 digits long.

Dubslow · 2012-03-02, 16:41

If GIMPS also found a prime, you'll have to add that to your list

2010-10-05, 21:14	#1
rogue "Mark" Apr 2003 Between here and the 15460₈ Posts	World Record Factorial Prime Found From http://www.primegrid.com/forum_thread.php?id=1336: A remarkable discovery was made yesterday in PrimeGrid's PRPNet. Dmitry Domanov found a World Record Factorial prime. 94550!-1 is prime and is 429,390 digits long. It enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Factorial primes and 155th overall. This is only the 24th known Factorial prime...the 14th discovery in the last 29 years and the first in almost 8 years. Needless to say, this is a very rare find. It more than triples the size of the previous record of 34790!-1 (142891 digits).

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2010-10-05, 21:37	#2
paulunderwood Sep 2002 Database er0rr 2·2,243 Posts	Here is a fixed link: http://www.primegrid.com/forum_threa...rap=true#26809 Could this be the biggest prime yet that uses general modular reduction? It's going to take several hours for The Prime Pages to confirm it's a prime Last fiddled with by paulunderwood on 2010-10-05 at 22:03

2010-12-20, 18:45	#5
axn Jun 2003 2²·3²·151 Posts	Late to the party, but this and this

2012-03-02, 14:38	#8
rogue "Mark" Apr 2003 Between here and the 2⁴×3×5×29 Posts	A new world record primorial has been found by PrimeGrid, http://www.primegrid.com/forum_thread.php?id=4146. It is 476,311 digits long.

2012-03-02, 16:41	#9
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 7221₁₀ Posts	If GIMPS also found a prime, you'll have to add that to your list