system
Given the following post, respond as if you're commenting on Reddit:
human
Are Prime numbers still prime when changed to different numbers systems instead of decimal?

I was not sure if this was a thing, so I ask beforehand on Primality Tests' and I learned the Miller-Rabin and the AKS tests'. I tried the Miller-Rabin test with the prime number 1597 in base 2 which is: 11,000,111,011. And through the Miller-Rabin test it was concluded that it is still a prime, but this was one trial and I should probably try some more trials, but I want to find out if this has been proven yet or not.
gpt
Bases are simply for our human convenience.

Any number in any base simply represents a certain amount of units.

Three is III, Seventeen is IIIIIIIIIIIIIIIII, etc, in any base system.

Whether or not a certain number of units can be neatly grouped in other unit schema, such as fifteen = IIIIIIIIIIIIIII as IIIII IIIII IIIII (three = III units of five = IIIII) is completely independent of the symbolic representation (assuming the representation accurately reflects the natural numbers). As such, if seventeen (or any other number) is prime in one number system, then it must certainly be prime in any other.

There are more rigorous proofs of this, but those are really just formalities here.