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