The Numbers Behind NUMB3RS by Keith Devlin

Author:Keith Devlin [Devlin, Keith]
Language: eng
Format: epub, mobi
Publisher: Penguin Group USA, Inc.
Published: 2007-11-14T05:00:00+00:00

A mod B

Thus, for example, 5 mod 2 is 1, 7 mod 4 is 3, and 8 mod 4 is 0.

As an example of the Fermat test, let us apply it to test the number 61 for primality. We need to calculate the number [260 – 1] mod 61, which can be written equivalently as [260 mod 61] – 1. If this is not zero, then 61 is not a prime. If it is zero, then 61 is either a prime or a pseudoprime (and in fact is a genuine prime, as we know already). We shall try to avoid calculating the large number 260. We start with the observation that 26 = 64, and hence 26 mod 61 = 3. Then, since 230 = (26)5, we get

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