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Roadmap for Understanding the 2020 Rigorous Proofs for Riemann Hypothesis, Polignac's and Twin Prime Conjectures

John Yuk Ching Ting, Rodney Williams

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Abstract

Nontrivial zeros and closely related two types of Gram points are computed directly from Riemann zeta function [or its proxy Dirichlet eta function]. Prime and composite numbers are computed, respectively, directly and indirectly from Sieve of Eratosthenes. All these well-defined [mutually exclusive] entities are characterized by Incompletely Predictable properties. For Riemann zeta function, its equivalent Euler product formula using product over prime numbers [instead of summation over natural numbers] faithfully represents this function. Thus, all prime [and, by default, composite numbers] are intrinsically encoded in Riemann zeta function. Considered as primary spin-offs, we provide succinct excerpts alluding to correct and complete mathematical arguments required to solve and explain intractable open problems in Number theory of Riemann hypothesis, two types of Gram points, Polignac's and Twin prime conjectures. This is achieved by utilizing the Complex Container concept and selected materials from the online published October 15, 2020 peer-reviewed research paper as listed in References of our expository paper. We logically philosophized there simply cannot have previous existing pure Number theorists as advocated experts in these particular open problems.

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Nontrivial zeros and closely related two types of Gram points are computed directly from Riemann zeta function [or its proxy Dirichlet eta function]. Prime and composite numbers are computed, respectively, directly and indirectly from Sieve of Eratosthenes. All these well-defined [mutually exclusive] entities are characterized by Incompletely Predictable properties. For Riemann zeta function, its equivalent Euler product formula using product over prime numbers [instead of summation over natural numbers] faithfully represents this function. Thus, all prime [and, by default, composite numbers] are intrinsically encoded in Riemann zeta function. Considered as primary spin-offs, we provide succinct excerpts alluding to correct and complete mathematical arguments required to solve and explain intractable open problems in Number theory of Riemann hypothesis, two types of Gram points, Polignac's and Twin prime conjectures. This is achieved by utilizing the Complex Container concept and selected materials from the online published October 15, 2020 peer-reviewed research paper as listed in References of our expository paper. We logically philosophized there simply cannot have previous existing pure Number theorists as advocated experts in these particular open problems.

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Available abstract

Nontrivial zeros and closely related two types of Gram points are computed directly from Riemann zeta function [or its proxy Dirichlet eta function]. Prime and composite numbers are computed, respectively, directly and indirectly from Sieve of Eratosthenes. All these well-defined [mutually exclusive] entities are characterized by Incompletely Predictable properties. For Riemann zeta function, its equivalent Euler product formula using product over prime numbers [instead of summation over natural numbers] faithfully represents this function. Thus, all prime [and, by default, composite numbers] are intrinsically encoded in Riemann zeta function. Considered as primary spin-offs, we provide succinct excerpts alluding to correct and complete mathematical arguments required to solve and explain intractable open problems in Number theory of Riemann hypothesis, two types of Gram points, Polignac's and Twin prime conjectures. This is achieved by utilizing the Complex Container concept and selected materials from the online published October 15, 2020 peer-reviewed research paper as listed in References of our expository paper. We logically philosophized there simply cannot have previous existing pure Number theorists as advocated experts in these particular open problems.

Key concepts: Riemann zeta function, Riemann hypothesis, Mathematics, Number theory, Twin prime, Prime (order theory), Function (biology), Prime number

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