Abstract
It is practically impossible to break a cryptosystem like RSA if the key is large enough with the prime numbers are randomly distributed. Recent research shows prime numbers show a certain distribution pattern. This makes it practically possible to break such systems by solving the factoring problem. By computing the distribution probabilities and finite field incremental changes of connected prime numbers, we have validated Robert J. Lemke Oliver and Kannan Soundararajan's study findings on trailing prime numbers. We proposed and developed ranked selection algorithm on prime number distribution. We developed a number of applications, including proposing one for fast factoring the product of two large prime numbers, also known as the factoring problem.
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