20-101 Serge Dolgikh

Prime Harmonics and Twin Prime Distribution (463K, PDF) Nov 27, 20

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Abstract. 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 the twin primes 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 approach and the bounds 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.

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