Titanic Prime whose Digits are all Prime

Theorem
The integer defined as:


 * $7352 \times \dfrac {10^{1104} - 1} {10^4 - 1} + 1$

is a titanic prime all of whose digits are themselves prime.

That is:
 * $\underbrace{7352}_{275} 7353$

Proof
It is clear that the digits are instances of $7$, $3$, $5$ and $2$, and so are all prime.

It is also noted that it has $275 \times 4 + 4 = 1104$ digits, making it titanic.