The Chaotic House of Primes and the Unprovable Riemann Hypothesis: Full Edition (Paperback) (ISBN-13: 9798391527237)

The title "The Chaotic House of Primes and the Unprovable Riemann Hypothesis" states the objectives. The aims of this work are:

• to capture the structure in which prime numbers find their place (the house);
• to analyse the findings in the context of the Riemann hypothesis, findings that attest to its non-verifiability;
• to emphasize the distribution of prime numbers, a distribution that is not random, not regular, but chaotic and generative of order.

By leveraging the complementarity between the set of prime numbers and the set of composite numbers, it is possible to capture the structure in which prime numbers reside using the ordered structure of composite numbers. Said ordered structure is in fact described by two formulas capable of generating sequences of only odd composite numbers.

Graphical representations follow to better grasp the regularity of composite numbers, as well as the spaces left by them free where the prime numbers find their "house".

It is therefore possible to shed light on the distribution of prime numbers and both support and contradict a particular aspect of the Riemann hypothesis, namely the assumption that prime numbers are distributed with regularity.

This leads to the thesis that the Riemann hypothesis is impossible to prove or disprove due to the "falsely ordered" nature of prime numbers. Their nature is neither ordered nor random, but chaotic and generative of order, the true order of composite numbers which, due to their complementarity with prime numbers, make the latter appear ordered as well. These are the conclusions.

The text concludes with two annexes. In particular, using the algebraic form of the two previously mentioned families of sequences generating composite numbers, the first annex formalizes definitions of primality, of a sequence of prime numbers, and of the set of prime numbers; the second annex, instead, proposes a polynomial sieve for determining whether a number is prime.

Author: Giulia Rappoccio,Federico Romagnoli
ISBN-13: 9798391527237
Publisher: Independently Published
Language: English
Published: 06/06/2022
Pages: 36
Format: Paperback
Weight: 0.18lbs
Size: 9.00h x 6.00w x 0.09d