Problem 430

Erdős Problem #430: declared status 'open'. Formalized: no. Fix some integer $n$ and define a decreasing sequence in $[1,n)$ by $a_1=n-1$ and, for $k\geq 2$, letting $a_k$ be the greatest integer in $[1,a_{k-1})$ such that all of the prime factors of $a_k$ are $>n-a_k$. Is it true that, for sufficiently large $n$, not all of this sequence can be prime? Prize: no. Tags: number theory.