New Scientist Enigma 938 – Trios of Primes
by Richard England
From Issue #2093, 2nd August 1997 (link)
Harry, Tom and I were trying to find sets of three two-digit prime numbers such that if we added any two numbers of the set together the answer was double a prime. Within each set the three prime numbers had to be different; but we each found that, having created a set, we could then create a second set with the same properties by changing just one of its primes.
One of my two sets was the same as one of Harry’s sets and the other was the same as one of Tom’s; their other sets were different.
(1) What were my two sets?
(2) Which set might we have found whose three primes do not appear in any other set?