There is a composite number that's the sum of three 3-digit primes of the following sort: The first and the last digit are each 1-digit primes, and the first two digits taken together, as well as the last two digits taken together, are each 2-digit primes.

What are the three 3-digit primes that sum to the composite number in question?

313+317+373=1003=17*59

For the 3 primes the last digit must be 3 or 7.
For the middle digit must be a 1,3,7 or 9
The first must be 2,3,5, or 7

Considering the Last two digits the only possibilities become 13, 17, 37, 73, or 97

Putting this together gives a list of 10 3 digit numbers of which only four (313, 317, 373 and 797) are prime.

Adding these in sets of 3 gives three primes: 1427, 1483, 1487.  The only composite is at the top.

Posted by Jer on 2009-03-31 10:58:13