Number Theory

    

Both the 1-Dimensional Line from Sieve of Eratosthenes and 2-Dimensional Trajectory from Riemann Zeta Function Have Centroids as Perfect Point Symmetry

Authors: John Yuk Ching Ting

From perspective of Number theory, Dirichlet eta function (proxy function for Riemann zeta function as generating function for all nontrivial zeros) and Sieve of Eratosthenes (as generating algorithm for all prime numbers) are essentially infinite series. We apply infinitesimals to their outputs. Riemann hypothesis asserts the complete set of all nontrivial zeros from Riemann zeta function is located on its critical line. It is proven to be true when usefully regarded as an Incompletely Predictable Problem. We ignore even prime number 2. The complete set with derived subsets of Odd Primes all contain arbitrarily large number of elements while satisfying Prime number theorem for Arithmetic Progressions, Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. Having these theorems satisfied by all Odd Primes, Polignac's and Twin prime conjectures are separately proven to be true when usefully regarded as Incompletely Predictable Problems.

Comments: 31 Pages. Finalized Preprint Version for submission to JNT dated July 7, 2024.

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Submission history

[v1] 2024-05-09 00:32:30
[v2] 2024-05-25 00:33:00
[v3] 2024-07-07 22:29:50

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