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2007 Pseudoprime Statistics to $10^{19}$
Jens Kruse Andersen, Harvey Dubner
Experiment. Math. 16(2): 209-214 (2007).

Abstract

A base-$b$ pseudoprime (psp) is a composite $N$ satisfying $b^{N-1}\equiv 1\pmod N$. We use computer searches to count odd base-3 psp near $10^n$ for $n$ up to 19. The counts indicate that a good approximation to the probability of a random odd number near $z$ being a psp is $P(z)=z^{-0.59}$. Integrating $P$ yields a psp-counting function, $Q(x)=(x^{0.41})/0.82$, which gives estimated counts close to known actual counts up to 10$^{\mbox{\ASF 19}}$, although these estimates are probably not valid for all $x$.

A table comparing pseudoprime counts up to 10$^{\mbox{\ASF 11}}$ for bases 2, 3, 5, 7, 11, 13, 17, is included.

Citation

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Jens Kruse Andersen. Harvey Dubner. "Pseudoprime Statistics to $10^{19}$." Experiment. Math. 16 (2) 209 - 214, 2007.

Information

Published: 2007
First available in Project Euclid: 7 March 2008

zbMATH: 1145.11009
MathSciNet: MR2339276

Subjects:
Primary: 11A99

Keywords: pseudoprime , Psp

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.16 • No. 2 • 2007
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