Prime number theorem (lower bound on the score functional): 0.99490 (previous 0.92129, AlphaEvolve)
Status
Not evaluated
Recorded on · arxiv.org
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
No DiscoverIA status yet; this does not mean nobody has checked it.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
The gist
For the lower bound on the score functional linked to the prime number theorem, Together AI and EinsteinArena agents give 0.99490, against 0.92129 for AlphaEvolve (June 2025); larger is better; no DiscoverIA status yet.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-ea-prime-number-theorem-r1
@misc{discoveria-ea-prime-number-theorem-r1,
author = {{DiscoverIA}},
title = {Prime number theorem (lower bound on the score functional): 0.99490 (previous 0.92129, AlphaEvolve)},
howpublished = {DiscoverIA registry, entry ea-prime-number-theorem},
note = {Status « Not evaluated », snapshot 1, recorded on October 12, 2026. new result},
year = {2026},
url = {https://discoveria.ai/en/fiche/ea-prime-number-theorem/#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: nobody yetReport an error
What has not been reviewed?
The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Key facts
- Claimed by
- Together AI et agents d'EinsteinArena (agent non nommé par la source pour la valeur du papier)
announced on Mar 2026 - Nature
- new result
- Field
- Mathematics (analytic number theory / partial functions and a constant tied to pi(x)·log x / x)
- Checked by
- the platform's public checker (a tool); no third party named
- Sources (domains)
- 6 : 2 read word for word, 4 links only
- This entry
- AI draft, not reviewed
To understand
Analogy
Imagine wanting to estimate how many prime numbers lie below a given limit, and tightening the bracket each time a new calculation rule is proposed.
What it changes
If the value holds, AlphaEvolve's score (0.92129, June 2025) would be clearly exceeded, at 0.99490. The repository already gave 0.994179 in March 2026, with 1 785 keys.
What remains unclear
The paper says it chose this problem because the best known human solutions are much better than those of AI: the previous record compared against is AlphaEvolve's, not the best human result. The verifier is a public program, not a third party. The online ranking shows 0.9976572852677297 (CodexProLong, 15 August 2026), different from the paper's value.
6 sources.
For experts
Sources(domains)
- primairearxiv.orgpage read word for word · consulted on Oct 12, 2026 ·
we additionally report the previous best known result and the current best result
- articletogether.aipage read word for word · consulted on Oct 12, 2026 ·
we currently have the best known results for the following problems
- depotgithub.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
Method
Status “not evaluated” recorded on 12 October 2026 from arxiv.org (page read, quotation checked word for word).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. DiscoverIA has recorded no independent evaluation as of this date.
Imagine wanting to estimate how many prime numbers lie below a given limit, and tightening the bracket each time a new calculation rule is proposed.
In the same set
EinsteinArena: a platform where AI agents tackle open problems with public verifiers · 16 entries
- Not evaluated : Third autocorrelation inequality: upper bound 1.4523 (previous 1.4556, AlphaEvolve)
- Not evaluated : Flat polynomials of degree 69: 1.28093 (previous 1.34093, AlphaEvolve)
- Not evaluated : Distance ratio of 16 points in the plane: 12.889230 (previous 12.889266, AlphaEvolve)
- Not evaluated : Prime number theorem (lower bound on the score functional): 0.99490 (previous 0.92129, AlphaEvolve)
- Not evaluated : Circles in a rectangle, 21 of them: sum of radii 2.365832255 (previous 2.365832133, AlphaEvolve)
- Not evaluated : Tammes problem (50 points on the sphere): 0.5134721 (previous 0.5134719, AlphaEvolve)
- Not evaluated : Edges versus triangles (minimum triangle density): -0.71171 (previous -0.71249, AlphaEvolve)
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
not evaluated: only the platform's public checker, no third party named
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
Related frontiers
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