January 12, 1986

	Although Peter Montgomery only promised 30 more factors, he sent
me 60 more, and they filled Page 37.  This is the second time that a
single factorer has filled a whole page.  In 1982-3, Baillie filled Page
15 completely.

	While Page 37 was being duplicated, I received a note from Mr.
Silverman with the factors (#1531-#1535) of 2,n+ for n = 283, 287, 289
and 299 that Montgomery found.  When these two factorers used ecm on the
c70 of 2,287+, they both found the p19 (#1532), but they both missed the
p17 (#1596 below).  Was this just chance, or is the p17 really harder
than the p19 for ecm to find?

	As of the bottom of Page 36 the full Appendix C contained 1957
composite numbers and Appendix A contained 1766 primes with more than 25
digits.  As numbers are factored Appendix C shrinks while Appendix A
grows.  I predict that by next summer Appendix A will have more entries
than Appendix C.

	Here is another New Year's prediction:  Notice that Montgomery
has left a few composite cofactors with fewer than 62 digits. I predict
that on Page 38 Silverman will factor some of these cofactors.

					Keep the factors coming!



					Sam Wagstaff