The Equivalent of the Goldbach Conjecture and "Even Number Is the Difference Between Two Prime Numbers"
Bibliographic record
Abstract
Goldbach conjecture can be described as "an even number is the sum of two prime Numbers,", this description is well known, the Canadian guy's book «the unresolved problems in number theory», put forward a conjecture which is contrary to goldbach: that "evens are the different between two prime Numbers", the difficulty of the conjecture is not less than goldbach conjecture, as also an unresolved problem.This paper, based on the promotion of chandra symmetric matrix, there is a natural number as long as there is any matrix at the same time don't appear in the matrix as well as the matrix beginning of 4 , thus making the conjecture set up, thus obtained the equivalent propositions of "an even number are the difference between the two primes" conjecture: 2mn + m + n and 2m + m+n + x (m, n for any natural number, x takes only one value at a time, is a fixed) Is these two formulas can show all the natural Numbers greater than 4 + x? If not, then the "even number is the difference between two prime Numbers" conjecture is true, which is the equivalent of the conjecture. And I get the equivalent proposition of golabach too! Mathematicians can turn to this description, as long as have the solution of this new description, the original conjecture will also be solved, the road of research also greatly broaden, mathematicians on the new description of the solution, in the process of research should be have some achievements.The difference between this equivalent proposition and the original conjecture is that the original conjecture is only a description of a concept, while the equivalent proposition tends to be digitized and formulated.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.005 | 0.020 |
| Scholarly communication | 0.006 | 0.015 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.017 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".