There is a composite number that's the sum of three 3digit primes of the following sort: The first and the last digit are each 1digit primes, and the first two digits taken together, as well as the last two digits taken together, are each 2digit primes.
What are the three 3digit 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 20090331 10:58:13 