Abstract: A new mathematical technique called the T-sequence is a primality testing method. A similar approach can be applied to perform fast factoring for numerous special cases, a method that can, in all likelihood, be extended to the general case, making possible a general and fast factoring algorithm. The same T-sequence can be used to construct a prime number formula and a good random number generator.

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.

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 aft numbers are widely used in all areas of industrial and scientific simulations.

Abstract: A data security method and apparatus that provides an exceptional degree of security at low computational cost. The data security arrangement differs from known data security measures in several fundamental aspects. Most notably, the content of the message is not sent with the encrypted data. Rather, the encrypted data consists of pointers to locations within a virtual matrix, a large (arbitrarily large), continuously-changing array of values. The encryption technique is therefore referred to as Virtual Matrix Encryption. Furthermore, the data security arrangement uses a very large key of one million bits or more which creates a level of security much higher than any other existing method. The key is not transferred but is instead created from a file of any size that is available on both a computer used to send a secure message and a computer used to receive a secure message.