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The Pseudoprimes to $25 \cdot 10^9$

Carl Pomerance, J. L. Selfridge and Samuel S. Wagstaff, Jr.
Mathematics of Computation
Vol. 35, No. 151 (Jul., 1980), pp. 1003-1026
DOI: 10.2307/2006210
Stable URL: http://www.jstor.org/stable/2006210
Page Count: 24
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The Pseudoprimes to $25 \cdot 10^9$
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Abstract

The odd composite $n \leqslant 25 \cdot 10^9$ such that $2^{n-1} \equiv 1 (\operatorname{mod n})$ have been determined and their distribution tabulated. We investigate the properties of three special types of pseudoprimes: Euler pseudoprimes, strong pseudoprimes, and Carmichael numbers. The theoretical upper bound and the heuristic lower bound due to Erdos for the counting function of the Carmichael numbers are both sharpened. Several new quick tests for primality are proposed, including some which combine pseudoprimes with Lucas sequences.

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