Conference rusure::math

404.0. ""most wanted" factorizations" by TOOLS::STAN () Sat Dec 14 1985 11:45

According to Shanks, the ten most wanted factorizations (see note 51.6)
published by Brillhart, et. al. in 1983 were found in 1984.  So if any of
you have been madly working away on these over the last two years -
you're out of luck.

Here are some references on recent factoring techniques:

R. P. Brent, An improved Monte Carlo factorization algorithm,
	BIT, 20(1980)176-184.

R. P. Brent and J. M. Pollard, Factorization of the eigth Fermat number,
	Math. Comp., 36(1981)627-630.

H. C. Williams, A p+1 method of factoring, ibid, 39(1982)225-234.

C. Pomerance, Analysis and comparison of some integer facoring algorithms,
	in Lensta and Tijdeman, Computational Methods in Number Theory,
	Mathematical Centre Tracts 154 and 155, Amsterdam, 1982
	(in part 1, pp. 89-139).

J. A. Davis and D. B. Holdridge, The quadratic sieve and the cryptosecurity
	of the QS algorithm, in Advances in Cryptology, Plenum Publishing,
	New York: 1984.

C. P. Schnorr and H. W. Lenstra, Jr., A Monte Carlo factoring algorithm with
	linear storage, Math. Comp., 43(1984)289-311.

J. Dixon, Factorization and primality tests, Amer. Math. Monthly, 91(1984)
	333-352.