1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689
The smallest pandigital number in a given base b is an integer of the form
The following table lists the smallest pandigital numbers of a few selected bases:
|Base||Smallest pandigital||Values in base 10|
In a trivial sense, all positive integers are pandigital in unary (or tallying). In binary, all integers are pandigital with the exception of 0 and numbers of the form (the Mersenne numbers). The larger the base, the rarer pandigital numbers become, though one can always find runs of consecutive pandigital numbers with redundant digits by writing all the digits of the base together (but not putting the zero first as the most significant digit) and adding x + 1 zeroes at the end as least significant digits.
Conversely, the smaller the base, the fewer pandigital numbers without redundant digits there are. 2 is the only such pandigital number in base 2, while there are more of these in base 10.
Sometimes, the term is used to refer only to pandigital numbers with no redundant digits. And in some cases, a number might be called pandigital even if it doesn't have a zero as a significant digit, for example, 923456781 (these are sometimes referred to as "zeroless pandigital numbers").
No base 10 pandigital number can be a prime number if it doesn't have redundant digits. The sum of the digits 0 to 9 is 45, passing the test for divisibility for both 3 and 9. The first base 10 pandigital prime is 10123457689; lists more.
For different reasons, redundant digits are also required for a pandigital number (in any base except unary) to also be a palindromic number in that base. The smallest pandigital palindromic number in base 10 is 12345678987654321.
Currently, two zeroless pandigital Friedman numbers are known: 123456789 = ((86 + 2 * 7)5 - 91) / 34, and 987654321 = (8 * (97 + 6/2)5 + 1) / 34.
While much of what has been said does not apply to Roman numerals, there are pandigital numbers: MCDXLIV, MCDXLVI, MCDLXIV, MCDLXVI, MDCXLIV, MDCXLVI, MDCLXIV, MDCLXVI. These, listed in , use each of the digits just once, while has pandigital Roman numerals with repeats.
Pandigital numbers are useful in fiction and in advertising. The Social Security Number 987-65-4321 is a zeroless pandigital number reserved for use in advertising. Some credit card companies use pandigital numbers with redundant digits as fictitious credit card numbers (while others use strings of zeroes).