Prime Harmonics and Twin Prime Distribution

Distribution of twin primes is a long standing problem in the number theory. As of present, it is not known if the set of twin primes is finite, the problem known as twin prime conjecture. An analysis of prime modulo cycles, or prime harmonics in this work allowed to define approaches in estimation of twin prime distributions with good accuracy of approximation and establish constraints on gaps between consecutive twin prime pairs. With technical effort, the bounds on the distance between consecutive prime pairs obtained in this work can prove sufficient to establish that the next twin prime exists within the estimated distance, leading to the conclusion that the set of twin primes is unlimited and reducing the infinitely repeating distance between consecutive primes to two. The methods developed in the study can be instrumental in future analysis of prime distributions