<p>I always have to think about it on SATs and ACTs.</p>
<p>Just because. It's part of the definition of a prime number.</p>
<p>1 is what is called a unit; it is neither prime nor composite. The reason is that it violates many properties primes have. </p>
<p>For example, if one were prime, prime factorization would not be unique: 12 could be factored as 2<em>2</em>3 or 1<em>2</em>2*3, or with arbitrarily many leading 1s.</p>
<p>Many theorems applying to primes do not hold for 1 as well. Take Wilson's for example, which says that (p-1)! == -1 (mod p), where == is the congruence sign. With p = 1, we have 0 == -1 (mod 1), but that doesn't make sense. I wonder who first realized that 1 shouldn't be called prime.</p>
<p>EDIT: Probably Euclid.</p>
<p>In some sense Wilson's theorem does hold for 1, because a == b (mod 1) just means 1 divides a-b, therefore all numbers are congruent, mod1.</p>
<p>how come everything is credited to euclid!!??!?!</p>
<p>a prime number has two distinct factors, 1 (1*1) does not have two distinct factors</p>
<p>1 is the loneliest number...it has no other factor, it's oh so lonely.</p>
<p>One is the loneliest number that you'll ever do
Two can be as bad as one
It's the loneliest number since the number one
No is the saddest experience you'll ever know
Yes, it's the saddest experience you'll ever know
'Cause one is the loneliest number that you'll ever do
One is the loneliest number, whoa-oh, worse than two
It's just no good anymore since you went away
Now I spend my time just making rhymes of yesterday
One is the loneliest number
One is the loneliest number
One is the loneliest number that you'll ever do
One is the loneliest
One is the loneliest
One is the loneliest number that you'll ever do
It's just no good anymore since you went away</p>
<p>one by three dog night ... lol =)</p>
<p>According to a prep book...forgot which: "because an ancient (too far back into history to matter) mathematician said so".</p>