Sequence of Smallest Consecutive Composite Numbers longer than 100

Theorem
The $1$st prime gap greater than $100$ is between $370 \, 261$ and $370 \, 373$, of length $112$.

That is, the sequence of the smallest consecutive composite positive integers longer than $100$ is that of $111$ such, from $370 \, 262$ to $370 \, 372$.