T-sequence apparatus and method for general deterministic polynomial-time primality testing and composite factoring

Abstract

Using a new mathematical technique called the T-sequence, the inventor has discovered a powerful primality testing method that meets all four conditions above. A similar approach can be applied to perform fast factoring for numerous special cases, a method that can, in all liklihood, be extended to the general case, making possible a general and fast factoring algorithm. (Researchers heretofore have been able to factor only in sub-exponential time, never in polynomial time.) The same T-sequence can be used to construct a prime number formula (long sought after but never achieved) and a good random number generator. The former can be used to generate infinitely many prime numbers of any size efficiently, and the latter can generate non-periodic and absolutely chaotic random numbers. These numbers are widely used in all areas of industrial and scientific simulations. In general, the T-sequence can be used to handle efficiently the fundamental problems concerning prime numbers (which include primality testing, factoring, prime number formula, infinite-pattern prime problem, etc.).

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