Bibliographic record
Abstract
Based on the data we get, nlog n is acceptable approximation to A(Pn) for small Pn ( most of relative errors are on the order of 1%, 1‰ or 0.1‰ for Pn less than 2000 ), where Pn is the n-th prime for n ≥ 2 and A(Pn) = Ln − Pn but Ln is the largest strong Goldbach number generated by Pn. Thus we propose a proposition that A(Pn) ≈ nlog n for all Pn. To give indirect verification of the proposition for large Pn, we obtain an experimental formula for calculating the number of primes not greater than Pn relying on existence of A(Pn). Using the formula, our found relative errors are generally smaller than that arising from x/log x, for example, there is a found relative error to be about 0.00935% for the 382465573492-th prime but the relative error is about 3.45305% by x/log x, 0.16046% by x/((log x) − 1.08366), 0.02479% by x/log x + x/(log x)2 + 2x/(log x)3. If the proposition is proven, then Goldbach’s conjecture is true.
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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 | 0.004 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".