Mapes, Method
المؤلف:
Mapes, D. C.
المصدر:
D. C. "Fast Method for Computing the Number of Primes Less than a Given Limit." Math. Comput. 17
الجزء والصفحة:
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26-8-2020
1008
Mapes' Method
A method for computing the prime counting function. Define the function
 |
(1)
|
where 
is the floor function and the 
are the binary digits (0 or 1) in
 |
(2)
|
Legendre's formula can then be written
 |
(3)
|
The first few values of 
are
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.
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