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Q: When is the product of two prime numbers not a prime number?

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The product of two prime numbers is always a composite number, and it never is a prime number.

A composite number is the product of two or more prime numbers.

No.

The product of two numbers could be either a composite number or a prime number. If one of those numbers is 1 and the other is a prime number, the result is that prime number. If neither number is 1, the product of the two numbers will be a composite number. If one of those numbers is 1 and the other is not a prime number, the product will not be a prime number. So, in most cases, it will be a composite number.

No - because its factors include each of the two prime numbers.

The product of two prime numbers can never be another prime number, the numbers that you multiplied are factors of the product. (example, 9 times 5 is 45, 9 and 5 go into 45)

When one of the numbers is prime and the other is 1.

The greatest two-digit prime number is 97. The lowest two-digit prime number is 11. The product of the two numbers is equal to 1067.

The product of two prime numbers will be composite.

None of them can.

A semiprime or a prime square.

There are an infinite amount of such numbers.

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