Computational number theory has been in the news recently. On March 23, just before this review was finished, the New York Times printed an article on the anticipated completion of a project to factor RSA129, a 129-digit integer proposed as a challenge over fifteen years ago in connection with a cryptographic method for which cracking the code is equivalent to achieving such a factorization. The project may well be completed by the time this review is published. The calculation uses a

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... ted quadratic sieve method of Pomerance [P] (or see the final chapter of the book under review) that reduces the number of arithmetic operations required from the more than 1050 needed to check all possible prime factors by trial division to a mere 1017 or so.