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Yes, it is always. Assume temporarily that the product of two prime numbers is not always composite. This implies that that at least one product of prime numbers is also prime. Now, say two different prime numbers p and q, when multiplied, equal r. If r is a Prime number, then r's only positive factors are 1 and r. But 1 is not a prime number. This contradicts that both p and q are prime (because either p or q MUST be 1). Therefore, the product of two prime numbers is always composite.

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Q: Is the product of two prime numbers is always composite?
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