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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 ...

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally ...

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 ...

Suppose f(x) is a function of x that is twice differentiable at a stationary point x_0. 1. If f^('')(x_0)>0, then f has a local minimum at x_0. 2. If f^('')(x_0)<0, then f ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...

A modified Miller's primality test which gives a guarantee of primality or compositeness. The algorithm's running time for a number n has been proved to be as ...

If there exists a critical region C of size alpha and a nonnegative constant k such that (product_(i=1)^(n)f(x_i|theta_1))/(product_(i=1)^(n)f(x_i|theta_0))>=k for points in ...