Pseudoprime Statistics to $10^{19}$
Andersen, Jens Kruse ; Dubner, Harvey
Experiment. Math., Tome 16 (2007) no. 1, p. 209-214 / Harvested from Project Euclid
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.
Publié le : 2007-05-15
Classification:  Psp,  pseudoprime,  11A99
@article{1204905876,
     author = {Andersen, Jens Kruse and Dubner, Harvey},
     title = {Pseudoprime Statistics to $10^{19}$},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 209-214},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204905876}
}
Andersen, Jens Kruse; Dubner, Harvey. Pseudoprime Statistics to $10^{19}$. Experiment. Math., Tome 16 (2007) no. 1, pp.  209-214. http://gdmltest.u-ga.fr/item/1204905876/