The prime triplet (2, 3, 13) is interesting in that it can produce six primes using a product with a sum or difference:

2 + 3*13 = 41

3 + 2*13 = 29

13 + 2*3 = 19

3*13 - 2 = 37

2*13 - 3 = 23

13 - 2*3 = 7

Prove this is the only such prime triplet.