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The Decision Problem*

Published online by Cambridge University Press:  03 November 2016

R. L. Goodstein
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Extract

There are many questions in mathematics to which an answer can be found by a purely mechanical procedure. For instance we can determine the valid statements of the class of the statements

n is prime

by the sieve of Eratosthenes; the numbers 2, 3, 4 and so on up to any assigned n are written in a row, and we begin by striking out every second number, starting with 2. Of those which are left, the first is 3 and 3 is prime. Starting with 3, we then strike out every third number, and the first of those which remain is 5, which is prime. Starting with 5 we strike out every fifth number, determining the prime 7, and so on.

Type
Research Article
Information
The Mathematical Gazette , Volume 41 , Issue 335 , February 1957 , pp. 29 - 38
Copyright
Copyright © Mathematical Association 1957

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Footnotes

*

A lecture delivered at the 1955 meeting of the British Association for the Advancement of Science.

References

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