Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis

[AlexFekken]

"no current HP programmable calculator is fast enough to find the number in a reasonable amount of time"

Are you sure? Perhaps you are right, but there are some obvious ways to cut down the number of required calculations quite a bit, as compared to a naive brute force attack. E.g. you could calculate the number of different values of n^3 mod 1000 (and then mod 10^6, then mod 10^9) that only contain the required digits. I would expect that that could narrow down the search quite a bit...