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Prime Number Races

2006· article· en· W2964347707 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueAmerican Mathematical Monthly · 2006
Typearticle
Languageen
FieldMathematics
TopicAnalytic Number Theory Research
Canadian institutionsUniversity of British ColumbiaUniversité de Montréal
Fundersnot available
KeywordsFiguringPrime (order theory)MathematicsValue (mathematics)ArithmeticPure mathematicsCombinatoricsPhysicsStatistics

Abstract

fetched live from OpenAlex

This talk is a survey of “prime number races”. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x than there are of the form 4n+1. Similar observations have been made with primes of the form 3n+2 and 3n+1, primes of the form 10n+3, 10n+7 and 10n+1, 10n+9, and many others besides. More generally, one can consider primes of the form qn + a, qn + b, qn + c, . . . for our favorite constants q, a, b, c, . . . and try to figure out which forms are “preferred” over the others – not to mention figuring out what, precisely, being “preferred” means. We describe these phenomena in greater detail and explain the efforts that have been made at understanding them. This talk should be accessible to graduate students. 1272547773

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.768
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.003

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.

Opus teacher head0.025
GPT teacher head0.336
Teacher spread0.311 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it