Note to Newcomers to this Project Here is a short description of the "Pages". The sequence numbers in the left column count factorizations found since 1981. Next come the label 651 (2,651+ means 2 + 1) and the size (c209 means 209 decimal digits) of the number which was factored. Then come the new factor(s), the discoverer and the method used. Recently, only the multiple polynomial quadratic sieve (ppmpqs), the elliptic curve method (ecm) and the number field sieve (nfs) have been used. `hmpqs' stands for hypercube multiple polynomial quadratic sieve. Under `new factors', `p90' means a 90-digit prime and `c201' is a 201-digit composite number. The LM notation is explained in the book. From time to time I issue a list of `champions'. These are the TWO greatest successes so far for each factorization method. For methods whose time depends just on the size of the number factored, the measure is the size of that composite number. For methods whose time depends on the size of the (prime) factor discovered, the measure is the size of that factor. We use four categories to measure the success of nfs. The first measure for the special nfs is simply the size of the number factored (and whose factors were unknown). The second measure for snfs is "by snfs difficulty." Simple snfs uses a polynomial p(X), constructed using the special form of the number N factored, and a zero m of p modulo N. The "snfs difficulty" of N is the size of p(m), which is a multiple of N. The general nfs would factor any number of given size in about the same time. It ignores any special form the number might have. Its performance is measured fairly by the size of the number factored. The hybrid s/gnfs has features of both special and general nfs. Its performance is measured by the size of the number factored. Every measure, except the first measure for snfs, tries to reflect the computational labor required by the factorization. The first column gives the sequence number of the report of the factorization. The list of champions usually also shows the first five holes (unfactored numbers) in each of the eighteen tables. The `wanted' lists were prepared by J. L. Selfridge, and now I make these lists. The numbers on the lists are the most desired (for psychological reasons) factorizations. Often they are early holes (unfactored numbers) in their tables. Sometimes their exponent has special form, like a power of 2 or a prime. Keep the factors coming! Sam Wagstaff Department of Computer Sciences Purdue University West Lafayette, IN 47907-1398 email: ssw@cerias.purdue.edu