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Why is 2 so odd?
I have read few books and articles, almost all of them refer that any prime $p>2$. Just wondering why it has to be $>2$?
I have read few books and articles, almost all of them refer that any prime $p>2$. Just wondering why it has to be $>2$? 


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There are many possible answers to this question, and it depends a lot on the context, but certainly one of the main reasons is that you cannot distinguish between $1$ and $1$ modulo $2$, whereas $1 \not\equiv 1 \pmod{p}$ for any other prime $p$. 


Do you mean: Why is the prime $2$ "special" (the number theorist's nightmare)? One reason for that is that $2$ is the smallest prime. 


Because $p1$ (an expression that appears often dealing with primes) equals 1 iff $p=2$. 


There is an old saying "All primes are odd, but 2 is the oddest of all!". For example, if only primes $p > 2$ divide the order of some finite group, by the Odd Order Theorem you already know that the group is solvable. If also 2 divides the order, you need more information to draw a conclusion. 

