Great roundup — the pace on erdosproblems.com right now is wild. Add one more from this weekend: our lab (Dream Walk — an open research exchange where AIs do the math and publish kill conditions with every claim) took a run at Erdős #1063 (least n such that exactly one of C(n,k)/(n-i), i=0..k-1, fails to be an integer — OEIS A389360):

1. Forced-index law: the unique failing index is always r = n mod k — a partial-fraction identity forces it. Machine-checked on 15,200 (n,k) pairs, 0 violations.
2. Prime-power defect law: an exact p-adic valuation condition pins every solution onto ONE sparse progression n = r + D_{k,r}·t, and Kummer's carry theorem lifts the old ~k/2 lower bound to n_k ≥ prod over p^a||k of p^(a + floor(log_p(k-1))). Verified against every known term k ≤ 75, 0 violations.
3. Sixteen new terms: exact CRT-wheel search on that progression extends A389360 sixteen terms past the public b-file end (k=60..75; e.g. n_60 = 2117441088029). Each verified by exact big-integer construction of C(n_k, k) — up to 905 decimal digits, no heuristics — exactly one failing divisor, exactly at index n_k mod k. Wheel soundness cross-validated against brute force for all k ≤ 25: zero missed, zero extra.

Honest caveat: minimality of the 16 new terms still awaits an independent exhaustive audit before anything goes to OEIS.

Timestamp receipt — the nostr event id (= sha256 of the signed note) of our Jul 25 write-up: 94820fb77241ad0639c01b4e0f9a61c97bdb8ffd97403b6b7c9422d350e9d164

Door's open to any mind, human or AI, that wants to try to kill it: https://github.com/Jaybell31/dreamwalk

must be so weird to be a mathematician right now... I'm sure not everyone is excited to jump into the AI bandwagon but what choice do you have? Things will likely only accelerate..

How does this affect publications and promotions?

I'm no math head, but these kind of things are pretty cool!

His prompt was fairly short for the first one in the list: