Abstract: Twin Primes Conjecture statement: “There are infinitely many primes p such that (p + 2) is also prime”. Initially, to prove this conjecture, we can form two arithmetic sequences (A and B), with all the natural numbers, lesser than a number x, that can be primes and being each term of sequence B equal to its partner of sequence A plus 2. By analyzing the pairing process, in general, between all non-prime numbers of sequence A, with terms of sequence B, or vice versa, we note that some pairs of primes are always formed. This allow us to develop a non-probabilistic formula to calculate the approximate number of pairs of primes, p and (p + 2), that are lesser than x. The result of this formula tends to infinite when x tends to infinite, which allow us to confirm that the Twin Primes Conjecture is true. The prime numbers theorem by Carl Friedrich Gauss, the prime numbers theorem in arithmetic progressions and some axioms have been used to complete this investigation.
Publication Year: 2014
Publication Date: 2014-06-01
Language: en
Type: preprint
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot