March 12, 1991

Several "Wanted" numbers were factored on Page 62. From the old wanted
lists of January, 1990, Bob Silverman factored the "More Wanted" number
2,436+ c96 and Arjen Lenstra and Mark Manasse, with the help of dozens
of other people and computers, factored the "Most Wanted" number
10, 142+ c116. These numbers were factored by the Quadratic Sieve
algorithm.

New wanted lists were issued with Update 2.4 last November and the
following numbers from those lists were factored: Bob Silverman
factored the "Most Wanted" number 10,151- c139 and the "More Wanted"
number 2,427+ c98 by the Elliptic Curve method.  With the same method,
he found a small factor of the "More Wanted" number 2,496+ c114.  Then
he finished the c88 cofactor with the Quadratic Sieve. The "More
Wanted" number 2,463+ c101 was factored by te Riele, Lioen and Winter
by the Quadratic Sieve. Arjen Lenstra, Manasse and the network are now
doing the c113 cofactor of 10,151-, which is still "Most Wanted".

The only numbers from the original 1925 Cunningham-Woodall tables which
have not yet been completely factored are a few base 2 numbers with
exponent < 500. Factorizations of numbers in this category on Page 62
are shown in # 3117, 3118, 3129, 3130, 3131, 3136 and 3157. Only
sixteen of these numbers remain unfinished. All sixteen appear on the
wanted lists of Update 2.4.

There was one new champion for factoring Cunningham numbers on this
page.  (Recall that a champion is one of the best TWO records in its
class.) The record was the factorization of 10,142+ c116 by the
Quadratic Sieve mentioned above. The number 2,463+ c101 mentioned above
was the largest number ever factored on a single computer by the
Quadratic Sieve method. It was done on one processor of a Cray Y-MP4.

The first holes done on Page 62 are in # 3129, 3133, 3137, 3138 and
3139. The second holes done on Page 62 are in # 3118 and 3120. The
third holes done on Page 62 are in # 3127 and 3128. The fourth holes
done on Page 62 are in # 3122, 3125, 3130, 3131, 3132 and 3157. The
fifth holes done on Page 62 are in # 3163 and 3170.

The smallest new factor reported on Page 62 has 21 digits. See # 3126.
The largest number in the full Appendix C was factored on Page 62. It
was 2,1187+ c357. See # 3121.

Bob Silverman has been working on the last few 92-digit numbers from
Appendix C.  Only one c92 remains and he is doing it now.

There was a typo in the "Most Wanted" list in Update 2.4. "2,279-"
should be "2,479-". Brent noticed that the "factor" 1717420766135846
should be omitted from the line for 2,591+ in Update 2.4 (and in Update
2.3). There was a single error which caused many typos in the Extension
to Table 3+ issued with Update 2.4. To conform to the shorthand used in
the book, delete "3L" and change "3M" to "3" inside parentheses in that
table extension.

Richard Crandall of NeXT Computer, Inc., reports finding the factor
2663848- 877152141313 of the Fermat number F_13 . The new cofactor is
composite.

At the request of several readers I have decided to issue a memo
explaining the Pages and Updates once a year. It is enclosed.

I have corrected several of your addresses recently. If you move,
please tell me.

Keep the factors coming!


Sam Wagstaff