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2 and 5 are one such pair.

Q: What are the pairs of prime numbers where their sum and difference are also prime numbers?

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Since 1, known as the "multiplicative identity", cannot be counted as a factor, there are many pairs of numbers that do not have common factors, such as 2 and 3, 2 and 5, and 3 and 5. There are many pairs of composite (not prime) numbers without common factors, such as 4 and 9. Also, since prime numbers do not have factors, any pair of primes cannot have a common factor, though a pair in which one number is prime may, e.g. 5 and 10.

There are no other prime numbers that are even but 2.

The only even prime number is 2.

They are prime numbers when you reverse the first one, the second one is prime also.

Yes. In general, if you have two different prime numbers, they will also be relatively prime.

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2+3,11+3,3+17

(2,3) and (2,5) are the two pairs such that the sum of their elements is a prime number.

You don't. All prime numbers are also whole numbers.

There are no other prime numbers that are even but 2.

Since 1, known as the "multiplicative identity", cannot be counted as a factor, there are many pairs of numbers that do not have common factors, such as 2 and 3, 2 and 5, and 3 and 5. There are many pairs of composite (not prime) numbers without common factors, such as 4 and 9. Also, since prime numbers do not have factors, any pair of primes cannot have a common factor, though a pair in which one number is prime may, e.g. 5 and 10.

This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.

The only even prime number is 2.

They are prime numbers when you reverse the first one, the second one is prime also.

All prime numbers are odd numbers. If one were even, it would be divisible by two and would, therefore, not be prime.

It's not.

The numbers are relatively prime, or co-prime.

Yes. In general, if you have two different prime numbers, they will also be relatively prime.