D. Acknowledgements.

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Many persons have contributed to these tables in the long period of time in

which they have been built up. Among these we would especially like to thank David

Cantor, Robert Co_n, Ren_e De Vogelaere, Earl Ecklund, Richard Guy, Alexander

Hurwitz, Paul Morton, John M. Pollard, Raphael Robinson, Richard Schroeppel,

Henry Thomas, Vance Vaughan, and Peter Weinberger.

The impressive results of the last twenty-_ve years would not have been obtained

without easy access to computers. Accordingly we would like to express

our gratitude to the directors and the sta_s of the following computing establishments:

Mathematics Department, University of Arizona; Bell Telephone Laboratories,

Murray Hill; The Computer Center, UC, Berkeley; IBM, Yorktown Heights;

Northern Illinois University; University of Illinois; The Computer Center, Stanford

University; and the Computing Facility, UCLA.

There are four persons we would like to single out for special thanks. The _rst

is Hugh Williams, whose assistance in the _nal stages of factoring and primality

testing of large \hold-outs" has been most helpful. The second is Mike Morrison,

who has assisted us at several stages of the work and who set up at Northern

Illinois University the factoring program which he and JB developed at UCLA.

This program, and its later automatic version due to Marvin Wunderlich and SSW,

were of signal importance in much of our primality testing, as well as in the factoring

of all composite numbers in the tables with no more than 50 digits.

The third person is Marvin Wunderlich, who has been so energetic in developing,

maintaining and using the factorization program and the primality testing

program DOWNRUN at DeKalb in conjunction with JLS. His work with the authors

and with the Cunningham Project stands behind many of the results here,

not the least of which is the collection of primality proofs in Appendix B, a large

portion of which are due to DOWNRUN.

The fourth person is Emma Lehmer, who, except for her insistence to the

contrary, would have been listed among the authors of this work. To have worked

with her and thereby to have bene_ted from her cheerful and e_ective involvement

in all the stages of this work has put us very much in her debt. We wish to express

our deep appreciation to her.

III E REFERENCES lxxiv

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