Home
Search Site
Largest
Finding
How Many?
Mersenne
Glossary
Prime Curios!
email list
FAQ
Prime Lists
Titans
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 ]
 GP2001
 A. Granville and C. Pomerance, "Two contradictory conjectures concerning Carmichael numbers," Math. Comp., 71 (2002) 883908. MR 1 885 636
Abstract:
Erdös conjectured that there are x^{1o(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 persontoperson discussions) that Erdös 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 Erdös and the results of Alford, Granville and Pomerance.
