N is an 11digit 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, nonsingle digit primes must end with one of the four odd digits: 1, 3, 7 or 9.
Thus, one can begin with the 11digit base ten pandigital number 10123456789 and proceed to higher numbers to find
the smallest 11digit base ten pandigital prime to be 10123457689.
And, one can begin with the 11digit base ten pandigital number 98876543201 and proceed to lower numbers to find
the largest 11digit base ten pandigital prime to be 98876532401.

Posted by Dej Mar
on 20100121 16:54:16 