# Finding the Integer

**Number Theory**Level 5

For any integer \(k\ge1\), 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 \(n\ge0\). Find the smallest positive integer, \(t\) such that \(x_t=2090\).