## Factor-by-mail project

From: bobs@mathworks.com (Bob Silverman)

Date: 1 Nov 1995 15:42:25 -0500
I post this message periodically in search of CPU cycles:

I am currently running a factor-by-mail project whose purpose is
factor some numbers on the MOST/More wanted list of the Cunningham
project. These numbers are of the form a^n +/-1 and have strong
historical interest, especially for a = 2.

We are currently doing 2^527-1, which is the smallest unfactored
number of the form 2^n-1. We will do 2^521 + 1 next.

This work is being accomplished with the Number Field Sieve.

If you are interested in helping out, please let me know.
I will send code and data.

I will also make available the current tables which show
all the factorizations done so far on this project.

Here is the current wanted list. It has been rather extensively
attacked with the Elliptic Curve Method. It is unlikely that
any of these numbers have any small (< 35 digits) factors.
Thus, NFS is the current method of choice.

Ten most wanted:

1. 2,1024+ C291 DONE Richard Brent, 10/20/95 by ECM. A surprise.
2. 5,256+ C134
3. 2,521+ C140
4. 2,527- C145 sieving
5. 2,563- C146
6. 10,163- C138 DONE
7. 10,158+ C120
8. 3,313+ C129 final stages
9. 3,316+ C127 DONE
10. 3,317+ C151 DONE

Twenty-four more wanted:
2,559- C142 2,934L C133 2,524+ C119 2,962M C116
2,974L C144 2,536+ C156 2,556+ C134 5,233- C148
5,223+ C129 5,226+ C157 6,199- C122 6,209- C111
6,206+ C146 6,209+ C130 6,256+ C195 7,187- C121
7,181+ C114 10,163+ C139 11,142+ C141 11,146+ C132
11,148+ C147 12,137- C123 12,139- C119 12,148+ C156

Bob Silverman,
The MathWorks Inc.,
24 Prime Park Way,
Natick, MA.