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A Prime Triplet (Posted on 2012-05-19) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Brian Smith    
Rating: 4.6667 (3 votes)

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Question re: Prime solution (?'s) | Comment 3 of 5 |
(In reply to Prime solution by Math Man)

(You left out the possibility of two 2's but this is dispensed of very easily)

You lost me on all of  the modular arguments:

If c=0 mod 7, then c=7, but |6-c|=1, which is not prime.

|6-35|=29 which is prime.  (I know |2*35-3| is not but that's not my point.)  How you you know c=7 is the only member of c=0mod 7 that you need to check?

  Posted by Jer on 2012-05-19 23:21:10

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