Titanic Prime whose Digits are all 0 or 1

Theorem
The integer defined as:


 * $10^{641} \times \dfrac {10^{640} - 1} 9 + 1$

is a titanic prime all of whose digits are either $0$ or $1$.

That is:
 * $\paren 1_{640} \paren 0_{640} 1$

where $\paren a_b$ means $b$ instances of $a$ in a string.

Proof
It is clear that the digits are instances of $0$ and $1$.

It is also noted that it has $640 \times 2 + 1 = 1281$ digits, making it titanic.