2014 AIME II Problem 15

For any integer k \geq 1, let p(k) be the smallest prime which does not divide k. Define the integer function X(k) to be the product of all primes less than p(k) if p(k)>2, and X(k)=1 if p(k)=2. Let \left\{x_{n}\right\} be the sequence defined by x_{0}=1, and x_{n+1} X\left(x_{n}\right)=x_{n} p\left(x_{n}\right) for n \geq 0. Find the smallest positive integer, t such that x_{t}=2090.