If we delete the non-primes from $e$, is the resulting number transcendental?

Question

If we eliminate the non-prime single-digit numbers from $e$, and then smash the remaining numbers together to make a new number, is it transcendental?

Answer 1

Although not a direct answer to the posed question, if the goal is to generate transcendental numbers (as the OP expressed in a comment), then exploit the Gelfond-Schneider Theorem:

• If $\alpha$ and $\beta$ are algebraic numbers, with $\alpha \ne 0$ and $\alpha \ne 1$ and $\beta \notin \mathbb{Q}$, then $\alpha^\beta$ is transcendental.