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 \{x_n\} be the sequence defined by x_0=1, and x_{n+1}X(x_n)=x_np(x_n) for n\geq 0. Find the smallest positive integer t such that x_t=2090.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.