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.

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.

It was checked that it is a prime number using the "Alpertron" Integer factorisation calculator on $6$th March $2022$.

This took approximately $2.5$ seconds.

According to David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$, this titanic prime was discovered by Harvey Dubner in $1984$, but this has not been corroborated.

At the time it was the largest such prime number known.

It needs to be investigated whether this record has been broken since then.

1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10^{641} \times \paren {10^{640} - 1} \mathop / 9 + 1$