Yes, 5883800000000000 is pandigital -- in base 14, where it's 75AD3621CB9408. No other pandigital number, in that or any smaller base, is divisible by a higher power of 10. Here's the latest version of my table, showing, for each small base, what's the highest power of each small number that divides any N-digit base-N pandigital number. (As always, this and every table should be viewed in a fixed-width font.) Base: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2: 1 0 3 1 11 0 5 2 21 0 29 1 36 0 7 3: 0 1 3 5 7 9 10 3 15 17 18 21 23 4: 0 0 1 0 5 0 2 1 10 0 14 0 18 0 3 5: 0 1 2 1 5 5 6 9 9 11 12 13 15 6: 0 0 3 1 1 0 5 2 8 0 3 1 13 0 7: 0 1 2 2 3 1 7 6 8 9 9 13 13 8: 0 0 1 0 3 0 1 0 7 0 9 0 12 0 2 9: 0 0 1 2 3 4 5 1 7 8 9 10 11 10: 0 0 1 1 3 0 5 2 1 0 8 1 11 0 11: 0 1 1 2 2 3 5 7 5 1 8 9 11 12: 0 0 1 0 1 0 2 1 6 0 1 0 10 0 13: 0 0 1 2 2 3 3 5 5 6 8 1 11 14: 0 0 1 0 1 0 2 1 6 0 1 9 1 0 15: 0 1 2 1 2 3 3 3 6 7 6 9 9 1 16: 0 0 0 0 2 0 1 0 5 0 7 0 9 0 1 Note that: For powers of any even number, bases that are congruent to 3 mod 4 have no solutions That's because in any odd base, a number is odd if and only if it has an odd number of odd digits. Any N-digit pandigital number of a length congruent to 3 mod 4 will have an odd number of odd digits, hence every permutation of those digits will represent an odd number. The diagonal values are all 1. That's because in an N-digit pandigital number, there's only one 0, and for a base-N number that digit has to go on the end for the number to be divisible by N. For divisors that are a power of 2, the values are the corresponding values for base 2, divided by which power of 2 it is, rounded down. For instance since the highest power of 2 in any 10-digit base-10 number is 21, the highest power of 16 (2^4) in any 10-digit base-10 number is 21/4 = 5. Analogously with powers of other divisors, e.g. powers of 3 vs. powers of 9 or of 27. That's because base 2^N numbers can be viewed as base-2 numbers chunked in sets of N base-2 digits. Analogously with powers of other divisors. For base N=2^M, the highest power of 2 that will divide an N-digit pandigital number is 2M-1. For instance in base 16 (2^4), it's 7. Again, that's because of chunking. In base 16 (hexadecimal), if the number ends with 80, that's 1000 0000 in base 2 (binary), as every programmer of my generation knows. That's seven 0s. There's no way to get more without a second hexadecimal 0. Questions that remain: Is there an efficient way to fill in the table for higher bases? Currently, I'm testing every N-digit base-N pandigital number for divisibility by every small prime. For each column, especially base 10, where's the first zero, i.e. the smallest number that no N-digit base-N pandigital number is divisible by? Which, if any of these rows and columns belong in OEIS? I don't think any of them are there yet. Where's the error in this post that I will notice immediately after I send it?