Number Theory


Mathematics for Incompletely Predictable Problems: Spin-Offs from Applying Information-Complexity Conservation to Sieve of Eratostheness

Authors: John Yuk Ching Ting

"Mathematics for Incompletely Predictable Problems" makes all mathematical arguments valid and complete in our previous paper (based on first key step of converting Riemann zeta function into its continuous format version) and this current paper (based on second key step of applying Information-Complexity conservation to Sieve of Eratosthenes). Nontrivial zeros and two types of Gram points calculated using this function plus prime and composite numbers computed using this Sieve are defined as Incompletely Predictable entities. Euler product formula alternatively and perfectly represents Riemann zeta function but utilizes product over prime numbers instead of summation over natural numbers. Hence prime numbers are encoded in this function demonstrating deep connection between them. Direct spin-offs from first step consist of proving Riemann hypothesis and explaining manifested properties of both Gram points, and from second step consist of proving Polignac's and Twin prime conjectures. These mentioned open problems are defined as Incompletely Predictable problems.

Comments: 21 Pages. Proofs for Polignac's and Twin prime conjectures.

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Submission history

[v1] 2019-09-29 17:17:10
[v2] 2019-10-21 00:13:22
[v3] 2019-10-22 16:37:36
[v4] 2019-10-23 06:25:42

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