We know that 2 is our only even prime number. My question is WHY?
Hellio, nycmath!
We know that 2 is our only even prime number.
My question is WHY?
If you know the definition of a Prime Number,
. . the reason should be obvious.
Consider the other even numbers: .$\displaystyle 4,\,6,\,8,\,10,\,\hdots$
All of them are composite numbers: .$\displaystyle (2\!\cdot\!2),\,(2\!\cdot\!3),\,(2\!\cdot\!4),\,(2 \!\cdot\!5),\, \hdots$
Just to extend the thinkung a bit - just as 2 is the only multiple of 2 that is a prime number, so also is 3 the only multiple of 3 that is prime, 5 is the only multiple of 5 that is prime, 7 is the only multiple of 7 that is prime, etc.
Well yes, you do quote the correct definition. That was not at all my point, go back and carefully read my post including the quote.
I quoted the post that said "An positive integer is prime if it has only one and itself as factors". That definition makes one a prime. Now it is common to use that definition; I once heard Keith Devlin use it in a talk.