Mathematics and engineering

Structure and Interpretation of Computer Programs is full of interesting footnotes. Here’s a good one about the Fermat test for prime numbers:

Numbers that fool the Fermat test are called Carmichael numbers, and little is known about them other than that they are extremely rare. There 255 Carmichael below 100,000,000. The smallest few are 561, 1105, 1729, 2465, 2821 and 6601. In testing primality of very large numbers chosen at random, the chance of stumbling upon a value that fools the Fermat test is less than the chance that cosmic radiation will cause the computer to make an error in carrying out a correct algorithm. Considering an algorithm to be inadequate for the first reason but not for the second illustrates the difference between mathematics and engineering.

Taken from page 53.


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