| @cdhmiamifan13: The reason 1 is not considered to be a prime number is that doing so would complicate the statement of many mathematical facts. For example, the fundamental theorem of arithmetic states that any positive integer can be written uniquely (that is, in one and only one way) as a product of prime numbers, if we ignore the order in which the prime factors are written. So, for instance, 2135 = 5 × 7 × 61, and that's the only way to write 2135 as a product of prime numbers (other than just rearranging the primes, like 7 × 61 × 5). If 1 were considered to be prime, this would no longer be true, because we could also write, say, 2135 = 1 × 5 × 7 × 61, or 2135 = 1 × 1 × 5 × 7 × 61, or whatever. So we'd have to rephrase the fundamental theorem of arithmetic to say that any positive integer can be written uniquely as a product of prime numbers *greater than 1*, to exclude these silly cases. It turns out that most statements about prime numbers are like this—if we considered 1 to be a prime number, we would have to specifically exclude it from these statements. It's easier just to define the term "prime number" to exclude 1 from the outset in order to avoid this awkwardness, by defining a prime to be a positive integer with exactly two distinct factors. |
Prime Numbers 
Literary Math 
Two Minute Math: LCM
