{"product_id":"the-chaotic-house-of-primes-giulia-rappoccio-9798391527237","title":"The Chaotic House of Primes and the Unprovable Riemann Hypothesis: Full Edition","description":"The title \"\u003ci\u003eThe Chaotic House of Primes and the Unprovable Riemann Hypothesis\u003c\/i\u003e\" states the objectives. The aims of this work are: \u003cul\u003e\n\u003cli\u003eto capture the structure in which prime numbers find their place (the house);\u003c\/li\u003e\n\u003cli\u003eto analyse the findings in the context of the Riemann hypothesis, findings that attest to its non-verifiability;\u003c\/li\u003e\n\u003cli\u003eto emphasize the distribution of prime numbers, a distribution that is not random, not regular, but chaotic and generative of order.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003eBy 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. \u003cp\u003e\u003c\/p\u003eGraphical 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\". \u003cp\u003e\u003c\/p\u003eIt 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. \u003cp\u003e\u003c\/p\u003eThis 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. \u003cp\u003e\u003c\/p\u003eThe 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Giulia Rappoccio,Federico Romagnoli\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9798391527237\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Independently Published\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/06\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 36\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.18lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.09d","brand":"Giulia Rappoccio","offers":[{"title":"Paperback","offer_id":48137086632191,"sku":"9798391527237","price":20.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_9f2d7c4d-f4aa-47ce-9ca1-116d6ee90ea9.jpg?v=1770166446","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-chaotic-house-of-primes-giulia-rappoccio-9798391527237","provider":"WR Book House","version":"1.0","type":"link"}