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

Home
Search Site

Largest
Finding
How Many?
Mersenne

Glossary

Prime Curios!
e-mail 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) 883--908.  MR 1 885 636
Abstract: Erdös conjectured that there are x1-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 x2/7 Carmichael numbers up to x, and gave arguments which even convinced Shanks (in person-to-person 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.
Prime Pages' Home
Another prime page by Chris K. Caldwell