2 [ Prime numbers and their properties ]

Find two such prime numbers that both their sum and their difference are also prime numbers.

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If both numbers are odd, then both their sum and difference will be even, and there is only one even prime number. This means that among the sought prime numbers, one must be even, that is, equal to 2. Therefore, the difference, the second number, and the sum are consecutive odd numbers. Among such numbers, one is necessarily divisible by 3. Thus, one of them is equal to 3. So, one of the numbers is 2, and the difference (or sum) is 3. The only possibility is that the sought numbers are 2 and 5.

## Answer

2 and 5.