April 23, 1986

	Although no `more' or `most wanted' numbers were factored on Page 43,

Silverman factored 6,113+ and 11,89-, which were the second holes in their

tables.  He also finished the c68's and did half of the remaining c69's.

Brent factored 2,401- on his birthday.  Happy Birthday, Richard!

	The only numbers smaller than 69 digits currently in Appendix C are

5,149+ c64 and 3,288+ c58.  Both will be done quickly.

	There is a typographical error in line # 1855 on Page 42:  Change

`p74' to `p41'.  Dan Shanks caught this typo.

	I am starting to plan Update # 4, which will be more than twice as

large as Update # 3.  I don't remember any new factors of Fermat numbers

since Update # 3.  If you know of any new ones, please send them to me soon.

Also, please tell me about any papers which appeared in print during the past

year which are relevant to the book.  I prefer not to refer to preprints in

the Updates.

					Keep the factors coming!





					Sam Wagstaff