47 and 3, 43 and 7, 37 and 13, 31 and 19
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Yes, it can. Examples are 2 and 5 to make 10 and 2 and 7 to make 14. If your question was if they could make an even prime number, the answer is no. Two is the only even prime number.
the two prime numbers will be factors of that number, which would make that number a composite number
The sum of any two prime numbers may or may not be prime. The sum of the two prime numbers 2 and 3 is the prime number 5, and the sum of the two prime numbers 5 and 7 is the composite number 12.
The product of two prime numbers is always a composite number, and it never is a prime number.
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.