Make a list of prime numbers, using the digits from 0 to 9 exactly once each in the list. What is the minimum sum of all the numbers in such a list? What's the minimum product of all the numbers in such a list?

Ok, first off, I'm discluding '0' b/c:
1) It is not prime, and
2) it can't be included in other numbers to make them, or it, prime. (e.g. --> 02 wouldn't count as a prime b/c, although it would add correctly, it wouldn't make sense trying to multiply it)
So, given this, make your list of numbers:
1 2 3 4 5 6 7 8 9
and reason the first few:
2, 3, 5, and 7, (remember that 1 is not prime)
leaving you with 1 4 6 8 9.
Looking through the single-digit primes, 2 is the only one that can be left alone, meaning that 3, 5, and 7 must have other numbers tacked on.  Try this:
2, 41, 53, 67, 89, all of which are prime.
Then add them together, and you get 252.
Multiply these numbers, and you get 25915198.
Having said that, the answers I came up with are minimums of 252 when added and 25915198 when  multiplied.

Posted by David on 2005-03-28 07:47:15