The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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This paper is divided into two parts. Part 1 first presents an old and charming number theoretic conjecture which has been generally believed or at least respected by the mathematical community for over 70 years. A probabilistic argument is then detailed which supports the opposite of this conjecture. A vast amount of computing has been recently done at various universities all over the world in order to investigate the plausibility of this conjecture and it was largely as a result of these computations that the negative argument was formulated. Part II of the paper discusses these computations and describes some of the problems which were encountered in this project. Not only were many hours of machine time consumed but hundreds of man-hours were spent book-keeping and “terminal- watching” because of the non-homogeneous character of the project. Finally, a software system is described which, when fully implemented, will provide the user with controlled but automatic job submission permitting number theoretic projects such as this to be carried out with much less constant attention.