Pi(x) Prime counting function

Pi(x) = Number of primes <= x. It can be computed by verious methods.

Here are some notes from my integer calculator program XICalc:

Pi(X) = Number of primes <= X by sieve or Lehmer:
This is the prime counting function, for every real x >= 0, Pi(x) is the number of primes p such that p <= x. For example Pi(5) = Pi(6) = 3. The 3 primes are 2, 3, and 5. For small x, the sieve of Eratosthenes is used, for large x, Lehmer's formula is used. This is the method to use unless you are testing PiL1(x) (slowest), PiM(x) (slow), or PiL(x) (fastest for large x).

And: Wolfram Functions Site -- PrimePi[x]

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This page accessed times since July 27, 2007.
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Changes last made on Monday, 06-Aug-07 20:47:29 PDT

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