By Paul Hoffman
An advent to the delights and demanding situations of recent arithmetic.
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Extra info for Archimedes' Revenge: The Joys and Perils of Mathematics
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Euclid long ago proved that the supply of primes is inexhaustible. His 2,300-year-old proof is still a paradigm of mathematical simplicity and elegance. Assume, said Euclid, that there is a finite number of primes. Then one of them, call it P, will be the largest. Now consider the number Q. larger than P, that is equal to the number 1 plus the product of thu consecutive whole numbers from 1 to P. In other words, Q = 1 + I x 2 x 3 . . x P. From the form of the number Q. it is obvious that no integer from 2 to P divides evenly into it; each division would leave a remainder of 1.
I'll show you who knows about large numbers," Archimedes thought, and for revenge he reportedly concocted a com26 Archimedes' Revenge 27 putational problem about grazing cattle whose solution requires numbers so large that it was not solved until recently. Moreover, it was solved not by man but by machine: the fastest computer in the world. The posing of the insanely difficult cattle problem is but one of many incredible exploits that made Archimedes a legend in his own time. C. the king of the city, Hieron, called on Archimedes, a relative, to expel the sixty enemy ships.
Archimedes' Revenge: The Joys and Perils of Mathematics by Paul Hoffman