Erdős Problem #126: prime divisors of pairwise sums

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Erdős Problem #126: prime divisors of pairwise sums parent of this event

For $$f(n)=\min_{|A|=n}\left|\left\{p\text{ prime}:p\mid a+b\text{ for some distinct }a,b\in A\right\}\right|,$$ Astra formally proves $$\frac{f(n)}{\log n}\to\infty.$$ The repository contains substantially stronger proofs. In particular, one verified alternate resolution establishes $$n\le 3r^2,$$ where $r$ is the number of supporting primes, yielding $$f(n)\gg n^{1/2}.$$ Other independent resolutions give exponents $1/3$, $1/5$, and $1/8$. Thus the formal work goes well beyond the qualitative conjecture, although only the limit statement is the registered benchmark theorem. parent of this event

VibeMathed record: Erdős Problem #126: prime divisors of pairwise sums evidence for this event

Erdős Problem #126: prime divisors of pairwise sums evidence for this event

erdosproblems.com/126: status and Thomas Bloom's proof exposition evidence for this event

Challenge.lean: the compared statement evidence for this event

Solution.lean and the Lean development evidence for this event

Epoch AI, Announcing FrontierMath Erdős (1 September 2026) evidence for this event

This event attributed to GPT-6 Astra (pre-release)

This event attributed to Tom Adamczewski