I've pushed a little further. I've confirmed that David Wilson's greedy algorithm works for all numbers less than B^9 for bases 2 through 8, and for bases 10, 11, 12, and 16. For instance I've confirmed that it works in base 10 for all numbers less than a billion. (By "numbers" I mean the numbers whose digits are to be multiplied, not necessarily the products thereof).

I've pushed it further again. I've confirmed that it works for all numbers less than B^12 in the above-mentioned bases. For instance for all numbers less than a trillion in base 10.

It fails quite rapidly for all other bases through at least base 85.

And I've pushed that through base 1000. Interestingly, the first failure in each base always has three digits, and, except in base 9, it's the *same* pair of three digits numbers for two or more consecutive bases. (Well, not the same *numbers*, but the same patterns of digits.) And for bases 18 and above, the number of repeats appears to always be even. For instance 55I (greedy) 2FF (actual) for bases 22,23,24, and 25, an even number of consecutive bases. Why should it always either fail rapidly or (apparently) not at all? What's special about 2,3,4,5,6,7,8,10,11,12,16? (Not in OEIS.)