A method for computing the Prime Counting Function. Define the function

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Mapes' method takes time , which is slightly faster than the Lehmer-Schur Method.

**References**

Mapes, D. C. ``Fast Method for Computing the Number of Primes Less than a Given Limit.'' *Math. Comput.* **17**, 179-185, 1963.

Riesel, H. ``Mapes' Method.'' *Prime Numbers and Computer Methods for Factorization, 2nd ed.*
Boston, MA: Birkhäuser, p. 23, 1994.

© 1996-9

1999-05-26