Siamese Twin primes Can someone edit my answer to this question whether I am answering the question or I am not? The question is > Let us say that two prime numbers $p$ and $q$ are siamese twins if $|p-q|=1$. List all the siamese twins that exist, and prove your list is complete. ### My answer For two prime numbers $p$ and $q$ are siamese twins if $|p-q|=1$. Assume, at least one in $p$ or $q$ is an even number. That even number is $2$. We, then let $q=2$. Therefore $|p-q|=1$, $p=1+q$, $p=1+2$, $p=3$. Thus there is only $2$ and $3$ siamese twin existed. Please I really need to know if I am answering what is asked in the question or not.

Your conclusion is correct but your explanation is flawed. You should not _assume_ that one of $p$ or $q$ is even, since this is a necessary intermediate conclusion: instead argue that one of them _is_ even, because they differ by $1$, and that one must equal $2$ because it is the only even prime.