No, you can apply any mathematical operation to a prime number.
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Because 2 is a prime number and 2 added to any other prime number will give an odd result.
5.
2 can be added to 5: 2+5 = 7
No, the sum of a prime number and a composite number is not always even.
You don't always. 2 + 5 = 7, for example. But all prime numbers other than 2 are odd and two odd numbers always equal an even number when added together.