First Occurrence of Prime Gap of 864

Theorem
The first occurrence of a prime gap of $864$ is between $6 \, 505 \, 941 \, 701 \, 960 \, 039$ and $6 \, 505 \, 941 \, 701 \, 960 \, 903$.

Proof
$6 \, 505 \, 941 \, 701 \, 960 \, 039$ is a prime number.

$6 \, 505 \, 941 \, 701 \, 960 \, 903$ is a prime number.

It can be checked that all numbers between these two are composite.

It can also be checked by computer that there is no prime gap of $864$ between smaller prime numbers.