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One of them is by 27 bigger than the first one and 14 smaller than the third one. What is the sum of these prime numbers?

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sqdancefan
Prime numbers that differ by an odd number must include 2 as one of them. Your numbers are ...
  2
  2+27 = 29
  29+14 = 43
Their sum is 2+29+43 = 74.