Erdős problem 821 · problems.science

Is it true that, for every $\epsilon>0$ , there exist infinitely many $n$ such that $g(n) > n^{1-\epsilon}$ ?

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4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

821.lean

Retained formal statement3 of 4

The best known bound is that there are infinitely many $n$ such that $g(n) > n^{0.71568\cdots}$ , obtained by Lichtman [Li22] as a consequence of proving that there are $\geq \frac{x}{(\log x)^{O(1)}}$ many primes $p\leq x$ such that all prime factors of $p-1$ are $\leq x^{0.2843\cdots}$ (which improves a number of previous exponents, most recently Baker and Harman [BaHa98]).

FormalConjectures/ErdosProblems/821.leanErdos821.erdos_821.variants.lichtman1 lineExact file

1∃ c > 0.71568, {n | ↑n ^ c < ↑(Erdos821.g n)}.Infinite

SolvedStatement only, no proof

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