Not evaluated
Erdős problem #679: proof improved by reducing dependence on the prime number theorem according to the wiki (Aristotle)
The gist
According to the teorth/erdosproblems wiki on AI and Erdős problems, Aristotle reportedly obtained an improved proof for problem #679 by reducing dependence on the prime number theorem (announced on January 12, 2026).
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . 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.
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-erdos-679-aristotle-1c-r1
@misc{discoveria-erdos-679-aristotle-1c-r1,
author = {{DiscoverIA}},
title = {Erdős problem #679: proof improved by reducing dependence on the prime number theorem according to the wiki (Aristotle)},
howpublished = {DiscoverIA registry, entry erdos-679-aristotle-1c},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-679-aristotle-1c#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The wiki files the entry under category 1(c) (AI building on literature known before and not rediscovered after) and cites DottedCalculator (2025) as prior literature. The prime number theorem estimates how many primes lie up to a given bound. Problem #679 belongs to number theory; the wiki marks the entry as partial progress, so the problem would be dealt with only in part if the proof held.
What remains unclear
The sources read do not say what the contribution adds to the earlier literature, or which proof it would improve. No independent verification is on record, and an addition published after the wiki's freeze would not appear there.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · wiki
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Wiki frozen
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Dated archive: status recorded on the wiki frozen on Jun 30, 2026
Sources
- Main sourcegithub.com · wikipage read word for word · consulted on Oct 12, 2026
- Reference listerdosproblems.comlink only, reading not recorded
- Corroborationterrytao.wordpress.compage read word for word · consulted on Oct 17, 2026 ·
We have created a github repository to coordinate this process
- Repositorygithub.com · CONTRIBUTING.mdpage read word for word · consulted on Oct 17, 2026 ·
this status is an unofficial crowdsourced classification of the problem
Method
Source: the “AI contributions to Erdős problems” wiki of the teorth/erdosproblems repository (a repository presented by Terence Tao in his blog post of August 31, 2025); frozen on June 30, 2026 (commit c8ad430, “freeze”) and read on October 12, 2026 in the git repository. Category 1(c), “AI building on literature” (literature known beforehand and not rediscovered afterwards; no significant human involvement). Humans named by the wiki: none; AI system: Aristotle. Date given by the wiki: January 12, 2026. Exact text: “Improved proof by reducing dependence on prime number theorem”; yellow flag (“partial progress”, according to the wiki's legend). Prior literature cited by the wiki: DottedCalculator (2025). Status of the problem in the teorth/erdosproblems community database (data/problems.yaml, unofficial classification, snapshot of October 12, 2026 with no commit identified, current state, not that of June 2026): open (informal_status=open); no formalised solution known (formal_status=unformalized). This status concerns the problem, not this contribution. Problem page not read by DiscoverIA: https://www.erdosproblems.com/679. DiscoverIA status: not evaluated (only the wiki's classification exists). Recorded on October 12, 2026.
Limits
DiscoverIA has not checked this contribution itself.
Key facts
- Claimed by
- Aristotle, according to the AI-Erdős wiki
announced on Jan 12, 2026 - Nature
- new result
- Field
- Mathematics (Erdős problem #679 (number theory))
- Wiki category
- AI building on literature (IA s'appuyant sur une littérature connue avant et non redécouverte après ; implication humaine non significative)
- Wiki verdict
- « Improved proof by reducing dependence on prime number theorem » : 🟡 progrès partiel (légende du wiki)
- Checked by
- no verifier identified
- Sources
- 4 : 3 read word for word, 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
An observation is added; none is ever erased.
In the same set
AI contributions to Erdős problems (wiki by T. Tao, frozen on June 30, 2026) · entry 274 of 521, by problem number
- Not evaluated : Erdős problem #672: partial results found in the literature according to the wiki (GPT)
- Not evaluated : Erdős problem #675: partial result according to the wiki (GPT-5.4 Pro)
- Not evaluated : Erdős problem #678: formalisation by Aristotle (proof: Cambie (2025))
- Not evaluated : Erdős problem #679: proof improved by reducing dependence on the prime number theorem according to the wiki (Aristotle)
- Not evaluated : Erdős problem #684: partial result according to the wiki (GPT-5.2 Thinking)
- Not evaluated : Erdős problem #684: partial result according to the wiki (GPT-5.4 Thinking)
- Not evaluated : Erdős problem #684: partial result according to the wiki (OpenAI internal model)
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