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Sure. All composite numbers can be written as a product of primes. It shouldn't be tough to find a composite number that's the sum of three other composite numbers.

Let's try 30. 2 x 3 x 5 = 30 Product of primes, check. 6 (2 x 3) + 10 (2 x 5) + 14 (2 x 7) = 30 Sum of three products of primes, check.

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Q: Can a product of primes be split into sum of three products of primes?
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