## Prime triples

Look at the following list of numbers:

1) 1,2,3:5,5,7
2) 1,2,9:11,11,19
3) 1,5,6:11,11,31
4) 1,5,8:13,13,41
5) 1,8,9:17,17,73
6) 2,3,5:11,13,17
7) 2,3,7:13,17,23
8) 2,3,13:19,29,41
9) 2,5,7:17,19,37
10) 3,4,5:17,19,23
11) 3,7,8:23,31,59
12) 5,7,8:43,47,61

Look closely at the numbers and determine how the three numbers to the left of the
colon generate the three primes to the right of the colon (this is the puzzle which is a minor challenge).

When you add up the three numbers to the right of the colon, you get another prime.
Also when you concatenate the numbers in the first group, you get 557 which is yet another prime.

I have a conjecture that you can generate an unlimited number of prime triples in the manner that I've done (that add up to yet another prime number). Offhand I don't know if any of the remaining 11 groups will yield a prime number when concatenated or if other prime triples exist that produce concatenated prime numbers. I just thought I would point these things out to the math explorers who want to go on further.