## A rose is a rose, but the prime factorization of 1 is not unique.

I mean, 1 = 1 *1

__or__1*1*1, whatever.

For sure, 7 is a prime number, right? But if 1 were a prime number, we'd have 7 = 1*7, 7=1*1*7, whatever. For sure, 12 is a composite number, right? It's composed

__uniquely__of prime factors 2*2*3. But if 1 were a prime number, we'd have 12 = 1*2*2*3, 12 = 1*1*2*2*3, whatever. Unfortunately, 1 is too promiscuous to be prime!

Hey, but it's not 1's fault, because 1 is the one-and-only

__unit!__And this one-and-only-unit is too fundamental to be either prime

__or__composite! That's pretty much the consensus nowadays, but famous mathematicians argued both sides well into the 20th century. Just ask Google "Is 1 a prime number?" and watch the sparks fly!

So who cares? Well, in case you haven't noticed, you

__can't__use Visual Basic to answer these questions! That's my point. A computer program can uncover

__facts__, but a computer program cannot develop

__insights__--any more than a hammer can design a house!

Sometime we will need to discuss the halting problem and the existence of undecidable propositions in computer science.

I mean, if you ask a computer program to find the last prime, and there

__is__a last prime, no problem. But if there

__is__no last prime, eventually smoke will come out of the ears of your computer!

Bottom line, finite computation cannot answer questions about infinity. And yet, Euclid showed thousands of years ago that there are always more primes. And a 9th grader can easily understand Euclid's straightforward argument today.

To check out Euclid's proof, Google "How do we know the prime numbers are infinite?"