"The Prime Glossary" is your Internet guide to the terminology of prime numbers. We began this project at The Prime Pages in early 1998 to provide simple, terse definitions of words and names related to prime numbers. When appropriate, the glossary includes links to other pages with fuller definitions and information.
The founding editor is Chris Caldwell--please address all comments and suggestions to him. New definitions are added weekly, let him know of any you would like to see added (or any definitions that you would like to write).
Comments on the goal and level of this glossary
This glossary is purposefully written on two levels because it is written to serve two audiences. First, for school teachers and students we wanted to define the basic words of elementary prime number theory and list the unusual or curious terms that could be the subject of excellent research papers. So we define terms using the least amount of jargon possible, even if this sometimes makes the wording slightly non-standard. For example, we might reword a definition so that we can use "divides" rather than "congruence" (even when the latter expression might be more natural to a mathematician). However, not all concepts can be easily defined.
Second, for those who are familiar with the basic terminology (say an undergraduate student in a number theory course), we wish to list some of the useful (but perhaps less well known) words and ideas. For this audience words that describe the typological qualities of numbers (for example), may seem frivolous--but they could provide an excellent test of analytic and heuristic skills as you answer the usual questions (are there infinitely many? can we quantify the number? generalize the concept?). Of course our site is concerned with prime number records, so we also try to provide links and references to sites that give the current results.
One of the best features of this glossary is that this dual nature is often found in a single definition. We might begin with a rough definition, then immediately move on to a technical version or advance consequences. This grants the university student immediate access to information and gives the school age student a peek down the grand road into the "Queen of Mathematics": number theory.