Bibliographic record
Abstract
The present paper describes a new method for the decomposition of integer numbers into their prime factors. To know if a number is prime, the classic and oldest method is to perform a series of Euclidean divisions by the prime factors in increasing order. In this article, I report a new and alternative method to the classic one. It is based on the fact that an even number that precedes a prime number must in no case have a potential prime factor that lacks a unit. This even number with one unit before the number to be decomposed can then be used to prove its primality or not by looking if it has a factor missing one unit. To achieve this, we divide the even by the prime factors (p) in ascending order and follow the decimal part. If the latter is equal to a ratio of (p - 1)/p (p is any prime factor), then the number to be decomposed is not prime and the prime number giving the ratio is its prime factor. This method has the potential to have applications in computer science and to lead to a new algorithm for decomposing numbers or further improve the performance of those existing.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".