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Albany Meetings (August 8-11)-Page 495

Notices

of the

American Mathematical Society

August 1983, Issue 227

Volume 30, Number 5, Pages 473-568

Providence, Rhode Island USA

ISSN 0002-9920

Calendar of AMS Meetings

THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was

sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri·

can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of

meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First

and second announcements of the meetings will have appeared in earlier issues.

ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to

the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet

ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the

office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of

the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab

stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below.

For additional information consult the meeting announcement and the list of organizers of special sessions.

MEETING ABSTRACT

NUMBER

DATE PLACE DEADLINE ISSUE

805 August 8-11, 1983 Albany, New York Expired August

(87th Summer Meeting)

806 October 28-29, 1983 Fairfield, Connecticut AUGUST 23, 1983 October

807 November 11-12, 1983 San Luis Obispo, California AUGUST 25, 1983 October

808 November 11-12, 1983 Evanston, Illinois AUGUST 29, 1983 October

809 January 25-29, 1984 Louisville, Kentucky NOVEMBER 2, 1983 January

(90th Annual Meeting) 1984

April 6-7, 1984 Notre Dame, Indiana

November 9-1 0, 1984 San Diego, California

January 9-13, 1985 Anaheim, California

(91 st Annual Meeting)

January

21-25, 1987 San Antonio, Texas

(93rd

Annual Meeting)

DEADLINES: Advertising

News/Special Meetings: (October Issue) September 8, 1983 (October Issue) August 22, 1983 (November Issue) October 6, 1983 (November Issue) September 19, 1983

Other Events Sponsored by the Society

June 5-August 13, 1983, Joint Summer Research Conferences in the Mathematical Sciences, University of

Colorado, Boulder, Colorado. January issue, page 74. July 11-29, 1983, AMS Summer Research Institute on Nonlinear Functional Analysis and Applications, University of California, Berkeley. April issue, page 332.

August

6-7, 1983, AMS Short Course: Population Biology, Albany, New York. This issue, page 496.

Subscribers' changes of address should be reported well in advance to avoid disruption of service: address labels are prepared

four to six weeks in advance of the date of mailing. Requests for a change of address should a/ways include the member or

subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of

address forms are not adequate for this purpose, since they make no provision for several important items of information which

are essential for the AMS records. Suitable forms are published from time to time in the Notices (e.g. June 1980, page 378). Send

change_ of address notices to the Society at Post Office Box 6248, Providence, RI 02940.

[Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American

Mathematical Society at 201 Charles Street, Providence, RI 02904. Second class postage paid at Providence, RI and additional

mailing offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society,

Post Office Box 6248, Providence, RI 02940.] Publication here of the Society's street address, and the other information in brackets

above, is a technical requirement of the U. S. Postal Service. The street' address should never be used by correspondents, unless

they plan to deliver their messages by hand.

Members are strongly urged to notify the Society themselves of address changes (in the manner described above), since (as

explained above) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the

AMS office.

Notices

of the American Mathematical Society

EDITORIAL COMMITTEE

Paul

F. Baum, Ralph P. Boas

Raymond L. johnson, Mary Ellen Rudin

Bertram Walsh, Daniel

Zelinsky

Everett Pitcher (Chairman)

MANAGING EDITOR

Lincoln K. Durst

ASSOCIATE EDITORS

Hans Samelson, Queries

Ronald L. Graham, Special Articles

SUBSCRIPTION ORDERS

Subscription for Vol. 30 (1983}:

$39 list, $20 member. The subscription price for members is included in the annual dues. Subscriptions and orders for AMS publications should be addressed to the American Mathematical

Society, P. 0. Box 1571, Annex Station,

Providence, Rl 02901. All orders must

be prepaid.

ORDERS FOR AMS BOOKS AND

INQUIRIES ABOUT SALES, SUBSCRIP

TIONS,

AND DUES may be made by

calling Carol-Ann Blackwood at

800-556-7774 (toll free in U.S.} between

8:00a.m. and 4:15p.m. eastern time,

Monday

through Friday.

CHANGE OF ADDRESS. To avoid

interruption in service please send address changes four to six weeks in advance. It is essential to include the member code which appears on the address label with all correspondence regarding subscriptions.

INFORMATION ABOUT ADVERTISING

in the Notices may be obtained from

Wahlene Siconio

at 401-272-9500.

CORRESPONDENCE, including changes

of address should be sent to American

Mathematical Society,

P.O. Box 6248,

Providence, Rl 02940.

Second class postage paid at

Providence, Rl, and additional mailing

offices.

Copyright © 1983 by the

American Mathematical Society.

Printed in the United States of America.

Volume 30, Number 5, August 1983

475 Recent Advances in Primality Testing,

Robert

Rumley

478 Mathematical Problems and Training in Robotics,

Jacob T. Schwartz and Micha Sharir

482 Mathematical Engineering: Problems and

Opportunities, Robert Hermann

485 News and Announcements

488 NSF News & Reports

491 Queries

492 Letters to the Editor

494 Election Information

495 Future Meetings of the Society

Albany, August 8-77, 495

Fairfield, October 28-29, 526

San Luis Obispo, November 77-72, 529

Evanston, November 77-72, 531

Call for Topics for 1985 Conferences, 533

Invited Speakers and Special Sessions, 536

539 Special Meetings

543

AMS Reciprocity Agreements (Supplement}

545

New AMS Publications

549 Miscellaneous

Personal Items,

549; Deaths, 549;

Visiting Mathematicians

(Supplementary List}, 550;

Backlog of Mathematics Research Journals, 552

555 AMS Reports and Communications

Appointments, 555; Reports of Past Meetings:

Norman,

555; New York City, 556;

Salt Lake City, 557; Officers and Committee

Members of the Society, 559

563 Advertisements

AMS Policy on Recruitment Advertising, 565

ElMS Subscription Forms, 567, 568

The following article is the sixth in the series of Special Articles published in the Notices. Its author, ROBERT RuMELY, was educated at Princeton University where he received his Ph.D. in 1978 with a thesis prepared under the supervision of Goro Shimura. He was a C.L.E. Moore Instructor at the Massachusetts Institute of Technology from

1978 to 1980 and a visiting postdoctoral fellow at Harvard University in 1981. Since 1981

he has been an assistant professor at the University of Georgia. His current research is in capacity theory on algebraic curves.

He has been awarded a Sloan Foundation Fellowship

for 1983-1984.

The series of

Special Articles was created to provide a place for articles on mathematical subjects of interest to the general membership of the Society. The Editorial Committee of the Notices is especially interested in the quality of exposition and intends to maintain the highest standards in order to assure that the Special Articles will be accessible to mathematicians in all fields. The articles must be interesting and mathematically sound. They are first refereed for accuracy and (if approved) accepted or rejected on the basis of the breadth of their appeal to the general mathematical public. Items for this series are solicited and, if accepted, will be paid for at the rate of $250 per page up to a maximum of $750. Manuscripts to be considered for this series should be sent to Ronald L. Graham, Associate Editor for

Special Articles, Notices of the American

Mathematical Society,

Post Office Box 6248, Providence, Rhode Island 02940.

Recent Advances in Primality Testing

by Robert Rumely

Prime numbers are one topic in mathematics

the public can relate to. People seem fascinated by the RSA "trap door" coding scheme, and by records for large primes. (Currently the largest known prime is the Mersenne number 2 8624

3 -1.)

Likewise, the primality test recently developed

by Adleman, Pomerance, and Rumely [1] has received a great deal of attention in the press.

That test, as significantly improved by Cohen and

Lenstra [2], is the main subject of this article.

Recent developments in commerce and security

aside, the problems of testing numbers for primality and factoring them have serious algo rithmic interest. It may be a surprise to some that much better methods are available for both than trial division up to y'n. Further, the two problems are distinct: it is possible to determine whether a number is prime or composite without attempting to factor it. In fact, it is very easy to decide as a practical matter whether a number is likely to be prime or composite. The idea is to apply a pseudo-primality test: to check a property (such as Fermat's congruence) which all primes share, but most composites do not. A number which is free of small prime divisors and which passes even a single pseudo-primality test is almost certain to be prime.

However, finding a rigorous proof of primality

or compositeness is more difficult. Some numbers of special form, such as Mersenne numbersquotesdbs_dbs47.pdfusesText_47

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