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 ]
C. Caldwell, "Unique (period) primes and the factorization of cyclotomic polynomial minus one," Mathematica Japonica, 46:1 (1997) 189--195.  MR 99b:11139
Abstract: Let b be an integer greater than one. For each prime p not dividing b, the expansion of 1/p (radix b) has a period dividing p-1. Unique primes are those primes (not dividing b) for which no other prime has the same period. Let Φn(x) be the nth cyclotomic polynomial. We develop criteria for when Φn(x)-1 is divisible by Φm(x), and use this to add 18 new primes (and 10 new probable primes) to the list of the 29 previously known unique primes (base 10). The divisibility properties found are useful in the search for primes of many forms.
Prime Pages' Home
Another prime page by Chris K. Caldwell <>