Remark: Family 011. The Ford–Konyagin–Luca conjecture on prime predecessors

Proves that the normalized ordered logarithms of the prime factors of $p-1$, counted with multiplicity, converge jointly to the Poisson–Dirichlet law $\mathrm{PD}(1)$ as $p$ ranges uniformly over primes up to $x$ and $x\to \infty$. This resolves the Ford–Konyagin–Luca conjecture. It also proves that infinitely many integers $n$ have more than $n^{1-\epsilon }$ totient preimages, for every $\epsilon >0$.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.