Reference Database
(references for the Prime Pages)
The Prime Pages

Search Site

How Many?


Prime Curios!
e-mail list

Prime Lists

Submit primes
This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

Item(s) in original BibTeX format

	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,
	year= 2002,
	mrnumber={1 885 636}

Prime Pages' Home
Another prime page by Reginald McLean