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@article{GP2001,
	author={A. Granville and C. Pomerance},
	title={Two contradictory conjectures concerning {Carmichael} numbers},
	abstract={Erd{\"o}s conjectured that there are $x^{1-o(1)}$ Carmichael numbers up to $x$,
		whereas Shanks was skeptical as to whether one might even find an $x$ up
		to which there are more than $\sqrt{x}$ Carmichael numbers. Alford, Granville
		and Pomerance showed that there are more than $x^{2/7}$ Carmichael numbers
		up to $x$, and gave arguments which even convinced Shanks (in person-to-person
		discussions) that Erd{\"o}s must be correct. Nonetheless, Shanks's skepticism
		stemmed from an appropriate analysis of the data available to him (and
		his reasoning is still borne out by Pinch's extended new data), and so
		we herein derive conjectures that are consistent with Shanks's observations,
		while fitting in with the viewpoint of Erd{\"o}s and the results of Alford,
		Granville and Pomerance.},
	journal= mc,
	volume={71},
	year= 2002,
	pages={883--908},
	mrnumber={1 885 636}
}