Number Choosing Contest.

Rule 3 talk:

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SpoilerWhen you mentioned python, I did think "Do we need to check other bases?" but I dismissed it, mainly due to the apparent straightforwardness of the other two rules. Thank you for doing that grunt work.

It's worth mentioning that rule 1 is also not large-number friendly.

And that rule 2, possibly, is prime-exclusive.

Edit: Number Ninja'ed.