I am thinking of a number

I am thinking of a number between $1$ and $10^{5}$ (inclusive) that is a palindrome. Let this number be $N$ . All of the following are true:

$\begin{cases} N \bmod 11 = 1 \\ N \bmod 17 = 13 \\ N\bmod 23 = 16 \end{cases}$

What is $N$ ?