N is an 11-digit base ten prime number N (with no leading zero) with the proviso that N contains each of the digits from 0 to 9 at least once.
Determine the respective minimum and maximum value of N.
In order to fail the divisibility test for 9 with the proviso that each of the digits from 0 to 9 occur at least once, the smallest additional digit is 1 and the largest additional digit is 8:
9+8+7+6+5+4+3+2+1+0+0 = 45 => 45 is divisible by 9,
9+8+7+6+5+4+3+2+1+0+9 = 54 => 54 is divisible by 9.
In addition, non-single digit primes must end with one of the four odd digits: 1, 3, 7 or 9.
Thus, one can begin with the 11-digit base ten pandigital number 10123456789 and proceed to higher numbers to find
the smallest 11-digit base ten pandigital prime to be 10123457689.
And, one can begin with the 11-digit base ten pandigital number 98876543201 and proceed to lower numbers to find
the largest 11-digit base ten pandigital prime to be 98876532401.
Posted by Dej Mar
on 2010-01-21 16:54:16