The Proof and Decryption of Goldbach Conjecture
In this paper, a few mathematical bases are given firstly. Then, the step thinness τp of primes is given as τp = Lo1 = P1ΠP/(P−1) for the inner character, having an lnX logarithmic outer character. The “best estimation and mutual exchange equivalent” are easily obtained as Lo1 = P1Π P/(P−1)~τp~lnX(ε...
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2023-08-01
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| description | In this paper, a few mathematical bases are given firstly. Then, the step thinness τp of primes is given as τp = Lo1 = P1ΠP/(P−1) for the inner character, having an lnX logarithmic outer character. The “best estimation and mutual exchange equivalent” are easily obtained as Lo1 = P1Π P/(P−1)~τp~lnX(ε). This is the principal contradiction, and P is the main aspect. Then, the sparsity τt of twin primes is defined as Lo2 = τt = P2 Π P/(P−2) = C2Lo1² = C2ln²X(C2 = 0.75739006). Then, the sparsity τg of the Goldbach pair and τb of both the twin and Goldbach pairs are obtained as Lo3 = τg = {2Lo1, Lo1², 2C2Lo1²} and Lo4 = τb =4.7Lo1³ (or they are omitted). Lastly, all conjectures can be proved with the same frame formula, N = X/LOK. The twin prime conjecture and Goldbach conjecture low bound are clearly and accurately proved with T = X/(C2Lo1²) = 1.32032X/ln²X and Gd = X/(2C2Lo1²) = 0.66016X/ln²X. Using Lo1 + C2 to decrypt the Selberg formula C(ω) = 2C(N) obtains the totally same results. |
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| spelling | doaj-art-8affd84eed5a4d21ae49bce034311f532025-08-20T03:43:37ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-08-01815210.3390/cmsf2023008052The Proof and Decryption of Goldbach ConjectureLinfu Ge0School of Computer, Southwest Jiaotong University, Chengdu 611756, ChinaIn this paper, a few mathematical bases are given firstly. Then, the step thinness τp of primes is given as τp = Lo1 = P1ΠP/(P−1) for the inner character, having an lnX logarithmic outer character. The “best estimation and mutual exchange equivalent” are easily obtained as Lo1 = P1Π P/(P−1)~τp~lnX(ε). This is the principal contradiction, and P is the main aspect. Then, the sparsity τt of twin primes is defined as Lo2 = τt = P2 Π P/(P−2) = C2Lo1² = C2ln²X(C2 = 0.75739006). Then, the sparsity τg of the Goldbach pair and τb of both the twin and Goldbach pairs are obtained as Lo3 = τg = {2Lo1, Lo1², 2C2Lo1²} and Lo4 = τb =4.7Lo1³ (or they are omitted). Lastly, all conjectures can be proved with the same frame formula, N = X/LOK. The twin prime conjecture and Goldbach conjecture low bound are clearly and accurately proved with T = X/(C2Lo1²) = 1.32032X/ln²X and Gd = X/(2C2Lo1²) = 0.66016X/ln²X. Using Lo1 + C2 to decrypt the Selberg formula C(ω) = 2C(N) obtains the totally same results.https://www.mdpi.com/2813-0324/8/1/52filter-siftersparsity density ? ?twin pairtwin bridgeGoldbach pairprincipal contradiction |
| spellingShingle | Linfu Ge The Proof and Decryption of Goldbach Conjecture Computer Sciences & Mathematics Forum filter-sifter sparsity density ? ? twin pair twin bridge Goldbach pair principal contradiction |
| title | The Proof and Decryption of Goldbach Conjecture |
| title_full | The Proof and Decryption of Goldbach Conjecture |
| title_fullStr | The Proof and Decryption of Goldbach Conjecture |
| title_full_unstemmed | The Proof and Decryption of Goldbach Conjecture |
| title_short | The Proof and Decryption of Goldbach Conjecture |
| title_sort | proof and decryption of goldbach conjecture |
| topic | filter-sifter sparsity density ? ? twin pair twin bridge Goldbach pair principal contradiction |
| url | https://www.mdpi.com/2813-0324/8/1/52 |
| work_keys_str_mv | AT linfuge theproofanddecryptionofgoldbachconjecture AT linfuge proofanddecryptionofgoldbachconjecture |