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. 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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 (October Issue) September 8, 1983 (November Issue) October 6, 1983 News/Special Meetings: (October Issue) August 22, 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. 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Notices of the American Mathematical Society Volume 30, Number 5, August 1983 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 475 Recent Advances in Primality Testing, Hans Samelson, Queries Robert Rumley Ronald L. Graham, Special Articles 478 Mathematical Problems and Training in Robotics, SUBSCRIPTION ORDERS Jacob T. Schwartz and Micha Sharir Subscription for Vol. 30 (1983}: $39 list, $20 member. The subscription 482 Mathematical Engineering: Problems and price for members is included in the Opportunities, Robert Hermann annual dues. Subscriptions and orders 485 News and Announcements for AMS publications should be addressed to the American Mathematical 488 NSF News & Reports Society, P. 0. Box 1571, Annex Station, 491 Queries Providence, Rl 02901. 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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 running time the public can relate to. People seem fascinated by the RSA "trap door" coding scheme, and by {2) exp(Cy'log n log log n). records for large primes. (Currently the largest In complexity theory, a problem is considered 8 24 known prime is the Mersenne number 2 6 3 - 1.) "tractable" if it can be solved by an algorithm Likewise, the primality test recently developed which runs in a polynomial number of steps in by Adleman, Pomerance, and Rumely [1] has the length of the input: {log n)c if the input is received a great deal of attention in the press. n. Thus, the APR algorithm just misses being That test, as significantly improved by Cohen and polynomial. Miller [6] has given a primality Lenstra [2], is the main subject of this article. algorithm which runs in polynomial time, but Recent developments in commerce and security depends on the Extended Riemann Hypothesis aside, the problems of testing numbers for for its correctness. Interestingly, because of primality and factoring them have serious algo­ the constants in the running time bounds, the rithmic interest. It may be a surprise to some that Cohen-Lenstra algorithm is faster than Miller's much better methods are available for both than for numbers of some tens to several thousands of trial division up to y'n.