Pair of Titanic Twin Primes

Theorem
The integers defined as:


 * $190 \, 116 \times 3003 \times 10^{5120} \pm 1$

are a pair of titanic twin primes.

That is:
 * $570 \, 918 \, 347 \paren 9_{5820}$

and:
 * $570 \, 918 \, 348 \paren 0_{5819} 1$

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

Proof
It is noted that these integers have $9 + 5820 = 5829$ digits, making them titanic.