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A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...

The notion of height is defined for proper ideals in a commutative Noetherian unit ring R. The height of a proper prime ideal P of R is the maximum of the lengths n of the ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

A maximal ideal of a ring R is an ideal I, not equal to R, such that there are no ideals "in between" I and R. In other words, if J is an ideal which contains I as a subset, ...

Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...