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Since there are infinitely many primes, there are infinitely many numbers that are products of 3 primes.
It's the product of the first three primes.
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.
8 has three primes (2x2x2) in its factorization, and 30 is the smallest number having three different primes (2x3x5) in its factorization.
There are not three odd primes with the sum of 14. The sum of three odd primes will be an odd number.