Two is a prime number.
One is NOT a Prime number. I think this was pretty clearly explained
by Euclid.
To be fair, you can define the 'prime numbers' to include one or not.
Both sets exist. But it simplifies a lot of theroems if you don't class
one as a prime numbner (as somebody said last night, if you include 1 in
the set of primes to get a lot of theorems for 'prime numbers other than
one', if you don't there are relatively few times where you have to say
'the set of prime numbers and 1'.
But I absolutely agree that most, if not all, mathematicians do not
include 1 i nthe set of prime numbers and it makes a lot of sense ot use
the same defintion as the rest of the world :-)
For some reason, they teach that one is a prime in schools ... why
... Wish I knew.
Having suffeed schools in the UK for many years, I have come to the
conclusion that just about everything I was taught, from 'A drird orange
is called an apricot' right up to 'A comparison is not a measurement'[1]
was downright incorrect. Fortunataely I had access to real books on the
subjects that interested me and read them...
[1] As I ahve said before, I would love to see a defintion of measurement
that does not involve comparison to a standard. That's what a measurement
_is_.
-tony