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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
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(1) |
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(2) |
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(3) |
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(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.