Prime values of f(a,b2) and f(a,p2), fquadratic
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Bibliographic record
Abstract
Dedicated to the occasion of John Friedlander's 80th birthdayWe prove an asymptotic formula for primes of the shape f (a, b 2 ) with a, b integers and of the shape f (a, p 2 ) with p prime.Here f is a binary quadratic form with integer coefficients, irreducible over and has no local obstructions.This refines the seminal work of Friedlander and Iwaniec on primes of the form x 2 + y 4 and of Heath-Brown and Li on primes of the form a 2 + p 4 , as well as earlier work of the author with Lam and Schindler on primes of the form f (a, p) with f a positive definite form.MSC2020: primary 11N32
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.012 | 0.001 |
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 it