On the numbers that determine the distribution of twin primes

• Main Author: Antonie Dinculescu
• Format: Article
• Language: English
• Published: University Constantin Brancusi of Targu-Jiu 2018-10-01
• Series: Surveys in Mathematics and its Applications
• Subjects: prime numbers; Twin Prime Conjecture; distribution of prime numbers; sieves
• Online Access: http://www.utgjiu.ro/math/sma/v13/p13_11.pdf

This paper is about a class of numbers indirectly connected to the twin primes, which have not been investigated so far. With the help of these numbers, we look at the set of twin primes from a different perspective and bring the reader's attention to some characteristics potentially useful in tackling the Twin Prime Conjecture. To this purpose, we simplify the problem by dividing the positive integers into two complementary sets: one whose members lead to a pair of twin primes by a simple algebraic operation but cannot be directly calculated, and another one whose members do not lead directly to twin primes but are responsible for their distribution and can be directly calculated. By analyzing the facts from the perspective of the numbers in the second set, we reveal some interesting patterns and properties that suggest new approaches to the problem.