October 15, 1985



	The multiple polynomial quadratic sieve method (mp-qs) and the

elliptic curve method (ecm) continue to romp through the Cunningham tables.

Two "Most" and one "More Wanted" factorizations were done in the past month.

Montgomery split 10,89+ and found one prime factor of 6,97+.  Silverman

finished off the remaining C59 of 6,97+ and also did 7,89+.  Both Montgomery

and Silverman factored many other numbers, too.  Dubner demonstrated that

the Brent-Pollard rho method is not obsolete yet.  Apparently, Suyama has

the first microcomputer program for ecm.  Wunderlich showed that Massively

Parallel Processors can factor numbers, too.

	There is a slight correction to my remarks about M(216091) in the

letter with Page 31.  Slowinski does not keep track of which exponents he

tests.  His feeling is that most of the exponents below 216091 have been

checked.  M(216091) took three hours on a Cray X-MP Model 24.  He ran the

Lucas-Lehmer test with a Schonhage-Strassen FFT multiply.



					Keep the factors coming!






					Sam Wagstaff