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.