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Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

If a number fails Miller's primality test for some base a, it is not a prime. If the number passes, it may be a prime. A composite number passing Miller's test is called a ...

Given a series of positive terms u_i and a sequence of positive constants {a_i}, use Kummer's test rho^'=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)) (1) with a_n=n, giving ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...

Baillie and Wagstaff (1980) and Pomerance et al. (1980, Pomerance 1984) proposed a test (or rather a related set of tests) based on a combination of strong pseudoprimes and ...

For some constant alpha_0, alpha(f,z)<alpha_0 implies that z is an approximate zero of f, where alpha(f,z)=(|f(z)|)/(|f^'(z)|)sup_(k>1)|(f^((k))(z))/(k!f^'(z))|^(1/(k-1)). ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...