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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 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)

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.

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

Every composite number ... that is, one that is not a prime ... can be written as the product of two or more prime numbers. The primes themselves are the exceptions. A prime number is the product of only ' 1 ' and itself, and ' 1 ' is not considered a prime number.

A semiprime or a prime square.

None of them can.

No. 15 is the product of two prime numbers: 3 and 5

The product of two prime numbers will be composite.