More Web Proxy on the site http://driver.im/

Search of the next prime of the form n!+1 & n!-1

The purpose of this page is to coordinate effort to search for the next primes of the form n!+1 & n!-1.

At the moment our purpose is to search the range between 30,000 -> 100,000.

All numbers in the range have been trial factored by Phil Carmody up to 6,320,124,029. The next step is perform a probable primality test to every remaining number. The number 35,000! is 143,845 digits long and the number 100,000! 456,574 digits.

Please join us in the search!

News Flash! I
On September 3, 2001, Ken Davis found 21480!-1 is prime!
This prime is 83727 digits long.

News Flash II !
On May 16, 2002, Leon Marchal found 34790!-1 is prime!
This prime is 142891 digits long.

News Flash! III
On May 22, 2002, Ken Davis found 26951!+1 is prime!
This prime is 107707 digits long.

News Flash!

There has been a P4 bug in the software, Please download the latest version here

My new email account is : nuutti.kuosa@kolumbus.fi, Currently I have not access to @hut.fi mail , but I try to read mails from that account during next few weeks.

What are known primes of the form n!+1 & n!-1

n!+1 is prime for n=1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477 and 6380 (21507 digits).

n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480 and 34790 (142891 digits).

More information about factorial primes can be found here or here.

Files section

Mid size number ranges available

Here is NEW Minus project

Here is a new assigning system.

Recently reserved ranges for that system

How you can help

Follow these steps :

1. Download the program called pfgw. You can use the command prompt version (PFGW.exe) or the windows version (WinPFGW.exe).

Both versions are in same zip file which you can download here .

2. Select one range from the bottom of this page and check that is not already reserved from the resently reserved ranges page.

Reserve it using the assigning system.

Check unfactored numbers in your range from the files area.

Create an input file, listing unfactored numbers in your range, in the pfgw directory.

(e.g. copy paste chosen numbers from the files area to a file: input.txt)

4. Start pfgw.

From the command prompt : pfgw.exe -l input.txt

Windows version : write the name of your input file in the command line box and press the start button. You have to select verbose mode from Output / Verbose menu. I recommend selecting both file and screen options.

In time Pfgw will finish the first number and write information to pfgw.out. It should look like this (if the number is not prime):

1964!-1 is composite: [5D8D35A763762B7] (26.538000 seconds)

When you have finished your range, mail your pfgw.out to me and reserve the next range.

If you stop primeform during your range using the stop button, then you unfortunately have to remove already completed lines from our input-file manually (the program always starts from the beginning of the input file).

Here's what you need to do. You can open your input file with a text editor and it will look as follows:

1950!-1
1951!-1
1952!-1

etc...

You have to check from your pfgw.out-file what was last number completed.

It could look like this:

1950!-1 is composite: [1AF6EB6D56E092C4] (26.438000 seconds)
1951!-1 is composite: [3268CE53836D415D] (26.588000 seconds)

Corresponding to the previous, you would delete the first two lines from your input-file (the lines that say 1950 and 1951)

If you have any questions, please don't hesitate to contact me. My e-mail address is :

nuutti.kuosa@hut.fi

Available ranges :

Number of candidates	File	Current searcher n!+1 = plus	Status	Current searcher n!-1 = minus	Status
43	Range 1	Rick Gaus	Done		n.a.
49	Range 2	Thomas Nøkleby	Done		n.a.
46	Range 3	Andrew Walker	Done		n.a.
43	Range 4	Francois ENOT	Done		n.a.
45	Range 5	Francois ENOT	Done		n.a.
40	Range 6	Johnson Lau	Done		n.a.
45	Range 7	Rob Bernhard	Done		n.a.
43	Range 8	Mark Dodrill	Done		n.a.
43	Range 9	Rick Gaus	Done		n.a.
45	Range 10	Ken Davis	Done		n.a.
46	Range 11	Ken Davis	Done		n.a.
43	Range 12	Andrew Walker	Done		n.a.
45	Range 13	Ken Davis	Done		n.a.
47	Range 14	Manuel Plaza	Done		n.a.
45	Range 15	Rick Gaus	Done		n.a.
44	Range 16	Reserved	Done		n.a.
43	Range 17	Francois Enot	Done		n.a.
47	Range 18	Francois ENOT	Done		n.a.
47	Range 19	Ken Davis	Done		n.a.
42	Range 20	David A. Miller	Done		n.a.
47	Range 21	Rick Gaus	Done		n.a.
46	Range 22	Rick Gaus	Done		n.a.
46	Range 23	Ken Davis	Done		n.a.
46	Range 24	Ken Davis	Done		n.a.
41	Range 25	Jani Leppä	Done		n.a.
44	Range 26	Francois ENOT	Done		n.a.
45	Range 27	Nigel Derby	Done		n.a.
47	Range 28	Ken Davis	Done		n.a.
45	Range 29	Lars Dausch	Done		n.a.
46	Range 30	Francois ENOT	Done		n.a.
47	Range 31	Rene Dohmen	Done		n.a.
47	Range 32	Rene Dohmen	Done		n.a.
46	Range 33	Rene Dohmen	Done		n.a.
42	Range 34	Ken Davis	Done		n.a.
41	Range 35	Rick Gaus	Done		n.a.
44	Range 36	Rene Dohmen	Done		n.a.
44	Range 37	Rene Dohmen	Done		n.a.
46	Range 38	Arkaidia Forsaith	Done		n.a.
42	Range 39	Arkaidia Forsaith	Done		n.a.
44	Range 40	Andrew Walker	Done		n.a.
45	Range 41	Rick Gaus	Done		n.a.
45	Range 42	Christ van Willegen	Done		n.a.
45	Range 43	Ken Davis	Done		n.a.
47	Range 44	Ken Davis	Done		n.a.
41	Range 45	Rick Gauss	Done		n.a.
43	Range 46	Ken Davis	Done		n.a.
45	Range 47	Gerry Winebrenner	Done		n.a.
38	Range 48	Thomas Pritchard	Done		n.a.
43	Range 49	Matthias Tobis	Done		n.a.
48	Range 50	Kevin O'Hare	Done		n.a.
45	Range 51	Ken Davis	Done		n.a.
44	Range 52	Ken Davis	Done		n.a.
44	Range 53	Niklas Vallaton	Done		n.a.
45	Range 54	Ken Davis	Done		n.a.
45	Range 55	Rich Gauss	Done		n.a.
45	Range 56	Goddess Junoesque	Done		n.a.
48	Range 57	Ken Davis	Done		n.a.
46	Range 58	Ken Davis	Done		n.a.
45	Range 59	Ken Davis	Done		n.a.
29	Range 60	Luigi Morelli	Done		n.a.
?	Range 30,000 - 34,000 !	Ken Davis	Done	Ken Davis	Done
?	Range 34,000 - 34,500 !	Lars Dausch	Done	Leon Marchal	Done
?	Range 34,500 - 35,000 !	34503!+1 -> 34598!+1 Done		Leon Marchal	Done
?	Range 35,000 - 35,500 !	Andrew Walker	Done	Leon Marchal	Done
?	Range 35,500 - 36,000 !	Andrew Walker		Leon Marchal	Done
?	Range 36,000 - 36,500 !	Andrew Walker		Leon Marchal	Done
?	Range 36,500 - 37,000 !	Andrew Walker		Leon Marchal	Done
?	Range 37,000 - 37,500 !	Jussi Heino		David Keeys
?	Range 37,500 - 38,000 !			Leon Marchal	Done
?	Range 38,000 - 38,500 !			Leon Marchal	Done
?	Range 38,500 - 39,000 !			Leon Marchal	Done
?	Range 39,000 - 39,500 !			Ian Brown
?	Range 39,500 - 40,000 !			Leon Marchal	Done
?	Range 40,000 - 40,500 !			Leon Marchal	Done
?	Range 40,500 - 41,000 !			Leon Marchal	Done
?	Range 41,000 - 41,500 !			Leon Marchal	Done
?	Range 41,500 - 42,000 !			Leon Marchal	Done
?	Range 42,000 - 42,500 !			Leon Marchal	Done
?	Range 42,500 - 43,000 !			Leon Marchal	Done
?	Range 43,000 - 43,500 !	Neil K		Leon Marchal	Done
?	Range 43,500 - 44,000 !			Leon Marchal	Done
?	Range 44,000 - 44,500 !			Leon Marchal	Done
?	Range 44,500 - 45,000 !			Leon Marchal	Done
?	Range 45,000 - 45,500 !	Klaus Moschner		Leon Marchal	Done
?	Range 45,500 - 46,000 !			Leon Marchal	Done
?	Range 46,000 - 46,500 !			Leon Marchal
?	Range 46,500 - 47,000 !			Leon Marchal
?	Range 47,000 - 47,500 !
?	Range 47,500 - 48,000 !
?	Range 48,000 - 48,500 !
?	Range 48,500 - 49,000 !
?	Range 49,000 - 49,500 !
?	Range 49,500 - 50,000 !
?	Range 50,000 - 50,500 !
?	Range 50,500 - 51,000 !
?	Range 51,000 - 51,500 !
?	Range 51,500 - 52,000 !
?	Range 52,000 - 52,500 !
?	Range 52,500 - 53,000 !
?	Range 53,000 - 53,500 !
?	Range 53,500 - 54,000 !
?	Range 54,000 - 54,500 !
?	Range 54,500 - 55,000 !
?	Range 55,000 - 55,500 !
?	Range 55,500 - 56,000 !
?	Range 56,000 - 56,500 !
?	Range 56,500 - 57,000 !
?	Range 57,000 - 57,500 !
?	Range 57,500 - 58,000 !
?	Range 58,000 - 58,500 !
?	Range 58,500 - 59,000 !
?	Range 59,000 - 59,500 !
?	Range 59,500 - 60,000 !

Last Modified : March 22, 2003