# 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.

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!

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).

Here is NEW Minus project

### How you can help

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 !