Karl Dickman (born 1862) published the only math paper in 1930 (age 68) about distribution of prime factors. He discovered the asymptotic distribution of the largest prime divisor of n, where n is chosen uniformly from $1,...,N$ and $N\to\infty$ (this is Dickman distribution). Much later the distribution of other prime divisors was described. This is related to the famous Poisson-Dirichlet distribution. (see also "The Poisson–Dirichlet Distribution and its Relatives Revisited" by Lars Holst).