Legendre's Formula PhiL(x, a)

PhiL(x, a) = Legendre's formula.

See: Legendre's Formula -- From MathWorld

Here are some notes from my program XICalc - Extra Precision Integer Calculator http://www.oocities.org/hjsmithh/download.html#XICalc :

PhiL(x, a) = Legendre's formula i.e., the number of integers in [1, x] not divisible by any of the first a primes. This function is used by the prime counting functions Pi(x), PiL(x), PiL1(x), and PiM(x). For values of a larger than about 13000, this function is prone to a Run-time error of "System.StackOverflowException was thrown", but this will not crash the program.

The algorithm for PhiL(x, a) can be found in the C# source file PrimeFA.cs in my program XICalc. See download link above.

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This page accessed times since Feb 17, 2006.
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Changes last made on Monday, 06-Aug-07 20:47:28 PDT