Question 403907: How many sets {a,b,c} of three prime numbers are there such that the sum of any two numbers from the set is also prime?
choose the answer and explain the reason to choose your response
infinitely many
no such sets
exactly one
more than one, but finitely many
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! None. Here's why:
If all three primes a, b, c are odd, then the sum of any two of them is a sufficiently large multiple of 2, not prime. If two of them are odd, then their sum is also even. However, if one or none of the primes are odd, this implies that at least two of a, b, c are equal to 2, and their sum is 4, which is also not a prime. Therefore there are no such sets.
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