# Amazing quintuples

$$5, 7, 17,$$ and $$19$$ are four prime numbers such that the sum of any three of them is also prime: \begin{align} 5+7+17&=29\\ 5+7+19&=31\\ 5+17+19&=41\\ 7+17+19&=43. \end{align} Are there 5 distinct positive primes such that the sum of any three of them is also prime?

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