Smallest Titanic Palindromic Prime

Theorem
The smallest titanic prime that is also palindromic is:
 * $10^{1000} + 81 \, 918 \times 10^{498} + 1$

which can be written as:
 * $1 \underbrace {000 \ldots 000}_{497} 81918 \underbrace {000 \ldots 000}_{497} 1$

Proof
It remains to be demonstrated that it is the smallest such palindromic prime greater than $10^{1000}$.