The Baillie-BPSW Primality Test is a probabilistic algorithm to determine the primality of a given integer up to several hundred decimal digits. This implementation is a fast efficient variant of that algorithm that has no known pseudoprimes.

Very fast System RPL functions for calculating the full integer values of Fibonacci Numbers, Lucas Numbers, and other Generalized Fibonacci recursive sequences. Source code, help text, and algorithm details included.

The PSSQ Algorithm accepts a prime p congruent to 1 mod 4 and returns the pair [x,y] such that the equality p=2+y^2 is satisfied. There can only be one such pair and this algorithm finds it very quickly, processing a 45-digit prime in less than half a second. Based on the algorithm devised by Stan Wagon with improvements by John Brillhart.