*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

The sum of Reciprocals of Primes diverges, but

(1) |

where is the Prime Counting Function and is the Euler-Mascheroni Constant (Le Lionnais 1983). Hardy and Wright (1985) show that, if is the number of distinct Prime factors of , then

(2) |

(3) |

(4) |

**References**

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hdmrd/hdmrd.html

Hardy, G. H. and Wright, E. M. *An Introduction to the Theory of Numbers, 5th ed.*
Oxford, England: Clarendon Press, 1985.

Le Lionnais, F. *Les nombres remarquables.* Paris: Hermann, p. 24, 1983.

Rosser, J. B. and Schoenfeld, L. ``Approximate Formulas for Some Functions of Prime Numbers.'' *Ill. J. Math.* **6**, 64-94, 1962.

© 1996-9

1999-05-25