Is there a prime of the given form?

primes of the form $$\lfloor p\cdot \pi^n \rfloor$$ with a prime $$\ p\$$ and a positive integer $$\ n\$$ play a role. For the prime $$\ p=19543\$$ , according to my calculations, a prime of this form must satisfy $$\ n\ge 21\ 000\$$, hence have more than $$\ 10\ 000\$$ digits.

Does a prime of the form $$\lfloor 19543 \cdot \pi^n\rfloor$$ exist and if yes, what is the smallest positive integer $$\ n\$$ doing the job ?

Simple brute force search in Maple reveals that smallest positive integer $$n$$ is $$25536$$, the probable prime being
$$\lfloor 19543 \cdot \pi^{25536}\rfloor = \underbrace{3236982484 \dots 5580309289}_{12700 \text{ digits}}$$
• Any reason to doubt Maple ? Anyway, I used the Miller-Rabin-test with $10$ random bases and the number passed it, hence is probably prime. – Peter Mar 24 at 12:31