# A Branch and Bound Solution for the Contrapositive Proof of the Riemann Hypothesis J.W. Helkenberg

#### 19 pages

Description A Branch and Bound Solution for the Contrapositive Proof of the Riemann Hypothesis by J.W. Helkenberg
November 16th 2010 | Kindle Edition | PDF, EPUB, FB2, DjVu, talking book, mp3, RTF | 19 pages | ISBN: | 9.54 Mb

Abstract:IFF the Riemann Zeta function (p) is an algorithm f.(p) whose analytic continuation results with a sequence of prime number occurrences resembling a list in a spreadsheet (q = the enumeration of Sloan’s A002410), WHERE [f.(p) = (q)], WHEREMoreAbstract:IFF the Riemann Zeta function (p) is an algorithm f.(p) whose analytic continuation results with a sequence of prime number occurrences resembling a list in a spreadsheet (q = the enumeration of Sloan’s A002410), WHERE [f.(p) = (q)], WHERE said spreadsheet is closed under some enumerable row limit (x), AND WHERE (x) is the total number of both prime AND composite row locations [(x) – (q) = (s)], AND WHERE (s) is the total number of composite row locations [(s) = (x) - (q)], AND WHERE [(q)/(x) = a/b = prime counting function], AND WHERE (q)0,-AND WHERE (¬ p) when taken as an algorithm f.(¬ p) produces a sequence, or list in a spreadsheet, of composite number locations (¬ q) arrayed in a column of a spreadsheet, said spreadsheet being closed under the same limit (x), AND WHERE [(x) - (¬ q) = (q)], AND WHERE each row (x, x+1, x+n) must contain a member that is either in the sequence of (q) or (¬ q)-THEN the algorithm f.(¬ p) is contradistinct to the algorithm f.(p).An algorithm is demonstrated for f.( ¬ p)- it is proven that the domain of the positive counting numbers (x, x+1, x + n ) can be modeled as a tree structure using modular arithmetic- the distribution of composite “ states” [(¬ q 1).

The zeros of the Zeta Function correspond with those leaf nodes (sequence given by [f.(p) = (q)]) that have neither parent nor child branches for the tree under consideration (See Sloan’s A181732 for a partial trace). The Prime Number Theorem is also given an exact bound, as the prime number spectrum decomposes into an arbitrarily scalable (branch and bound) fractal- from symmetries underlying the composite state distribution functions [f.( ¬ p)] the exact prime counting function becomes inherent.

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