Consecutive Primes

Define sum(N)\text{sum}(N) which returns the sum of digits of a number.

Find the smallest pair of consecutive primes aa and bb which such that sum(a)=sum(b)\text{sum}(a) = \text{sum}(b). Enter your answer as a+ba + b.

Details and Assumptions:

  • Consecutive prime numbers refers to a sequence of two prime numbers which don't have any prime number between them. For example: 2 and 3 are consecutive primes, 37 and 41 are consecutive primes.

  • As an explicit example: sum(37)sum(41)\text{sum}(37) \neq \text{sum}(41) because 3+74+13+7\neq 4+1. So 37 and 41 are not such numbers.

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