A modification of Legendre's Formula for the Prime Counting Function . It starts with

(1) |

where is the Floor Function, is the number of Integers with , and is the number of Integers with . Identities satisfied by the s include

(2) |

(3) |

Meissel's formula is

(4) |

where

(5) | |||

(6) |

Taking the derivation one step further yields Lehmer's Formula.

**References**

Riesel, H. ``Meissel's Formula.'' *Prime Numbers and Computer Methods for Factorization, 2nd ed.*
Boston, MA: Birkhäuser, p. 12, 1994.

© 1996-9

1999-05-26