The answer is 10.

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$\boxed{10} = 3 + 7 = 2 \times 5$

This is the smallest such number, since the number needs to be greater than all four primes, and the first four primes are 2, 3, 5, and 7. So it would need to be greater than 7. Also, the number needs to be the product of two distinct primes. Therefore 8 and 9 or out.