What is the largest prime with distinct digits? (It is certainly less than ten digits long.Can you explain it why?
This question depends on the number base being used. It is assumed that the OP meant base 10, but there is nothing special about that (or the answer) except that humans generally have ten fingers. Here are a few others in different bases:
- base 2: 10 (2)
- base 3: 201 (19)
- base 4: 103 (19, using all three non-zero digits always results in a number divisible by 3)
- base 5: 4302 (577, using all four non-zero digits always results in a number divisible by 2)
Higher bases are left as an excerise for the reader!