Mapes' Method
A method for computing the Prime Counting Function. Define the function
 | (1) |
is the Floor Function and the 
are the binary digits (0 or 1) in | (2) |
 | (3) |
are |  |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
 | |  | (9) |
 | |  | (10) |
 | |  | (11) |
Mapes' method takes time
, which is slightly faster than the Lehmer-Schur Method.See also Lehmer-Schur Method, Prime Counting Function
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.
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