Many problems in computational number theory require the application of some sieve. Efficient implementation of these sieves on modern computers has extended our knowledge of these problems considerably. This is illustrated by three classical problems: the Goldbach conjecture, factoring large numbers, and computing the summatory function of the M'{obius function.

Numerical Algorithms and Problems (acm F.2.1)
Sieves (msc 11N35), Goldbach-type theorems; other additive questions involving primes (msc 11P32), Factorization (msc 11Y05), Values of arithmetic functions; tables (msc 11Y70)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

te Riele, H.J.J. (1998). Computational sieving applied to some classical number-theoretic problems. Modelling, Analysis and Simulation [MAS]. CWI.