
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) A real number is an algebraic number if it is a zero of a polynomial with integer coefficients; and its degree is the least of the degrees of the polynomials with it as a zero. For example, the rational number a/b (with a, b and nonzero integers) is an algebraic number of degree one, because it is a zero of bxa. The square root of two is an algebraic number of degree two because it is a zero of x^{2}2. If a real number is not algebraic, then it is a transcendental number. The base of the natural logarithms e (2.71828...), and pi (3.14159....) are both transcendental. In fact, almost all real numbers are transcendental because the set of algebraic numbers is countable.
Chris K. Caldwell © 19992019 (all rights reserved)
