Erdős problem 371

Let $P(n)$ denote the largest prime factor of $n$ . Show that the set of $n$ with $P(n+1) > P(n)$ has density $\frac{1}{2}$ .

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

371.lean

Retained formal statement1 of 1

Let $P(n)$ denote the largest prime factor of $n$ . Show that the set of $n$ with $P(n+1) > P(n)$ has density $\frac{1}{2}$ .

FormalConjectures/ErdosProblems/371.leanErdos371.erdos_3711 lineExact file

1{n | (n + 1).maxPrimeFac > n.maxPrimeFac}.HasDensity (1 / 2)

OpenStatement only, no proof