The Poisson-Dirichlet law for prime predecessors

For a prime p chosen uniformly from $3\le p\le x$, list the prime factors of $p-1$ in decreasing order, with multiplicity. As $x\to \infty$, their logarithms, divided by $\log (p-1)$, converge in every finite joint distribution to the Poisson–Dirichlet distribution with parameter one. This proves the conjecture of Ford, Konyagin and Luca.