Under consideration for publication in J. Functional Programming 1 The Genuine Sieve of Eratosthenes Melissa E. O’Neill Harvey Mudd College, Claremont, CA, U.S.A. (e-mail: oneill@acm.org) Abstract A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes”. This paper shows that this example is not the s