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.

clearly number 2 is a must ,other wuse odd+odd-composite..

It easily to show that  if the other two do not include 3 thak one of the outcomes is a composite ,

 so 3 is a must.

  Mow let us check  2 3 5  , 2  3 7   and 2 3 11  we get composite results: 2*3-5, 7-2*3,  2+3*11

The prime triplet (2, 3, 13) qualifies.

Now we need to show that {2,3,p) for p>13 does not qualify. 

...Maybe later.

 

 

Posted by Ady TZIDON on 2012-05-19 12:07:17