CGI-BIN Number Theory Utilities Description

Number theory is the study of whole numbers and their properties.  (Number theory is sometimes also described as the study of integers and integer fields, an equivalent definition.)  Notions such as prime and composite numbers, as well as famous problems such as Fermat's last theorem, come from number theory.  Many famous mathematicians, such as Gauss and Euler, were number theorists or made substantial contributions to number theory.

Number theory is pivotally important in the digital age, as the difficulty of factoring a composite which is the product of large primes is the basis for RSA public-key cryptography.  Number theory also sometimes becomes a consideration in embedded control work, as microcontrollers deal most efficiently with integers and ultimately every input and output of a microcontroller is an integer.  Number theory sometimes enters into microcontroller arithmetic (rational approximation, for example) or into hardware design (ratiometric conversion in software, for example).

All of the CGI-BIN number theory utilities found at this site perform a calculation or a service which has as its basis number theory.

Number theory utilities generally require software to work with large integers.  All of the CGI-BIN number theory utilities at this site make use of the GMP library, a library for dealing with arbitrarily large integers and arbitrary-precision numbers.  Computer arithmetic with large integers is not a trivial matter, and much research has been done about how to efficiently multiply, divide, and perform other operations on large integers (for example, Karatsuba multiplication).  Using the GMP library for a CGI-BIN application also requires some technical savvy, and the details are here.

Additionally, all source code for the number theory utilities I've placed on the web is available here.

This web page is maintained by David T. Ashley.