January 31, 1986

	On Page 39 Montgomery continued to find an amazing number of base 2

factors.  Brent completely factored the second Mersenne number of which no

factors were previously known.  Suyama finished another Mersenne number.

	Smith and I factored a C61, McCurdy and Wunderlich factored the last

C62 and Silverman finished the C63's and the small cofactors that Montgomery

left.  As a result of this work, at the bottom of page 39 the smallest composite

number in Appendix C has 64 digits.

	There is a new champion for cfrac on Page 39; it is # 1692.  (The

second cfrac champion is # 1602.)  Suyama notes that Brent's P21 divisor of

2,439-, discovered before the sequence numbers began, is a champion for p+1.

For that P21, p+1 = 8.3.19.4673.13171.36037.121169 .

	Two corrections:  Delete C75 2,263- from the initial segment of Ap-

pendix C which was enclosed with Page 36.  In the cover letter with Page 37

it should say that the full Appendix C contains 1955 composite numbers--not

1957 of them.  These typos resulted from faulty editing of Appendix C in 1980.

					Keep the factors coming!



					Sam Wagstaff