You are requested to partition the set of 10 digits (0,1,…,9) into a maximal number of subsets, such that in each set it is possible to create a prime number
using all its members.

What is the highest prime thus created?

We want first as many primes as possible.  An upper bound on this is 6 because primes can end in 1, 2, 3, 5, 7, 9.
The leftover digits 0,4,6,8 would have to make the 1 and 9 actually become prime.  The best I came up with is to put the 4 with the 1 and the rest with the 9.

The subsets are then
2
3
5
7
41
8609

With 8609 being the largest prime.

Posted by Jer on 2014-05-16 10:31:41