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Because if they were even they would be a multiple of 2 and thus not prime.

Q: Why is every prime number greater then 2 an odd number?

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No. The first odd number, counting up from one, that is not a prime number, is 9.

Every single prime number Is odd , with the exception of 2 being an even number , but ... Not every single odd number is going to be prime. Example: 9-1,3,9

No.Consider that every prime number except 2 is an odd number.Consider also that the sum of two odd numbers is always an even number.Thus, the only case in which an odd number can be expressed as the sum of two primes is when it is 2 greater than a prime number, since it can take advantage of the only even prime number, 2.For example, 21 can be expressed as 2+19, both of which are primes. However, 27 has no such two primes, since 25 is not prime (5x5=25).

2 is the smallest prime number. It is co-prime with every odd number.

The sum of two prime numbers greater than 2 is an even number. The sum of 2 and any other prime number is an odd number.

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No. The first odd number, counting up from one, that is not a prime number, is 9.

That's not true.

Because every number is either odd or even. Even numbers are divisible by two, which means that (with the exception of 2 itself) they by definition are not prime.

Every single prime number Is odd , with the exception of 2 being an even number , but ... Not every single odd number is going to be prime. Example: 9-1,3,9

Because every number is either odd or even. Even numbers are divisible by two, which means that (with the exception of 2 itself) they by definition are not prime.

2 is the exception to the rule that every prime number is odd

Every prime number is odd except one: the number 2.

An even number because every prime number gretaer than 2 is odd.

No, take 9 for example. It has 1,9, and 3 as factors, so it's not prime.

All prime numbers other than 2 are odd numbers. 2 is the only even prime number.

No.Consider that every prime number except 2 is an odd number.Consider also that the sum of two odd numbers is always an even number.Thus, the only case in which an odd number can be expressed as the sum of two primes is when it is 2 greater than a prime number, since it can take advantage of the only even prime number, 2.For example, 21 can be expressed as 2+19, both of which are primes. However, 27 has no such two primes, since 25 is not prime (5x5=25).

It is not clear what you mean by "3p added by 1." If you mean 3p+1, there is only one such prime and that is 7, where p is 2. The reason is that every prime greater than 2 is odd and 3 times an odd number is odd and 1 plus that is even and no prime greater than 2 is even. If you mean 3p-1, the only prime is 5 for the same reason except that every odd number minus 1 is even. So again, 2 is the only value of p that produces a prime.