Formalize solutions to 40 more problems - #386
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As mentioned previously, I have formalized solutions to a bunch of Erdős problems. This batch updates the status of 40 more of these. I believe all of the formalizations are correct.
Of particular note: this batch includes https://www.erdosproblems.com/forum/thread/391 which caught me off-guard because I thought getting the exact constant$c$ would be tricky. However, the statement in the box only asks for "some constant $c>0$ such that $\frac{t(n)}{n} \leq \frac{1}{e}-\frac{c}{\log n}$ for infinitely many $n$ ", which this formalization does capture correctly! (It uses a simpler explicit value $c\approx 0.0002352$ rather than the optimal constant $c\approx 0.3044$ .) FYI, this formalization took about 9 hours with publicly-available GPT 5.6 Sol running at "Extra High" on Codex.