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| | Two Major Conjectures on Prime NumbersEasyChair Preprint 11717, version history| Version | Date | Pages | Version notes | 
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 | 1 | January 7, 2024 | 10 |  |  | 2 | January 8, 2024 | 13 | We improved much better the principal proof in the paper. |  | 3 | January 9, 2024 | 12 | This version is ready for peer-review |  | 4 | January 11, 2024 | 12 | This new version is clean, beauty and elegant. |  | 5 | January 13, 2024 | 11 |  |  | 6 | January 14, 2024 | 13 | We improved the manuscript again. | 
Keyphrases: Chebyshev function, Cramér's conjecture, Riemann hypothesis, Riemann zeta function, prime numbers | 
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