We need to translate Russian news post into natural English, format per rules.
First line: short headline under 90 chars, no markdown.
Then blank line, then body split into short paragraphs (2-3 sentences each), separated by blank lines.
Wrap few genuinely important facts — key numbers, percentages, drug/company/gene names, dates — in double asterisks . At most 4-5 per post, never a whole sentence.
Wrap study/journal citations and publication references in single underscores _ (e.g., Nature Aging, July 2026).
We need to preserve all facts, numbers, names, citations exactly. No commentary.
We need to identify important facts: numbers: 246, 17 августа (August 17), 2013, 70 миллионов (70 million), 600, Polymath8b, Lean 4, PrimeGapsLib, AxiomProver, Axiom Math, etc. Also date: August 17 (IEEE Spectrum reported). Also maybe "2013". Also "70 million". Also "600". Also "246". Also "Lean 4". Also "PrimeGapsLib". Also "AxiomProver". Also "Axiom Math". Also maybe "IEEE Spectrum". Also "Polymath8b". Also "2013". Also "70 million". Also "600". Also "246". Also "August 17". Also maybe "2026"? No.
We need at most 4-5 double asterisks. So we need to select only the most important facts. Probably: 246, 70 million, 600, August 17, 2013. That's five. Could also include Lean 4? But that's a tool name, maybe not needed as double asterisk? The rule says wrap key numbers, percentages, drug/company/gene names, dates. Company names could be considered? Axiom Math is a company; maybe we could wrap that. But we need at most 4-5. Let's choose: 246, 70 million, 600, August 17, 2013. That's five.
We must not wrap whole sentences. So we need to embed these within sentences, not wrap entire sentence.
Now citations: we have IEEE Spectrum article (August 17). Also maybe "Polymath8b" is a project, not a citation. There's no journal citation besides IEEE Spectrum (a magazine). We need to wrap study/journal citations and publication references in single underscores. So we should wrap IEEE Spectrum, August 17 maybe. Or IEEE Spectrum with date? The example: Nature Aging, July 2026. So we can do IEEE Spectrum, August 17. That is a publication reference.
Also maybe there is a citation for the Polymath8b project? Not a journal. So just that.
Thus we will have one underscored citation.
Now we need to produce body paragraphs, each 2-3 sentences.
Let's outline:
Paragraph 1: Axiom Math translated a proof into verifiable code: they formalized the bound that infinitely many adjacent primes are at most 246 apart. On August 17, IEEE Spectrum reported that the team published this formalization; the program checks the proof according to logical rules.
Paragraph 2: AxiomProver generated Lean 4 code, and project participants verified and compiled it into the library PrimeGapsLib. Its modules can be reused in future formal proofs.
Paragraph 3: The twin prime conjecture asks whether there are infinitely many prime pairs with difference two; this remains open. In 2013, Yitang Zhang proved that the gap between infinitely many consecutive primes can be bounded by 70 million. James Maynard reduced the bound to 600, and the Polymath8b project further reduced it to 246—the bound that Axiom formalized.
Paragraph 4: Ordinary proofs reside in article text and calculations. Axiom first created a detailed map of definitions, lemmas, and dependencies. Based on these formal goals, AxiomProver generated Lean 4 proofs, where the proof is written as a program and the checker verifies each step against logical rules. Participants then checked the code and organized it into the library.…
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GitHub
GitHub - AxiomMath/PrimeGapsLib: Lean formalization of bounded gaps between primes
Lean formalization of bounded gaps between primes. Contribute to AxiomMath/PrimeGapsLib development by creating an account on GitHub.
August 26, 2026 4
