I have a theory about the Prime Numbers.
It is sparked by Goldbach's (allegedly unproveable) Conjecture that all
even numbers are the product of two primes.
My theory is thus:
Since all even numbers are the product of two odd numbers,
And all prime numbers (except the number 2) are odd,
Primes must be redefined.
Old
Definition: Primes are numbers divisible only by themselves and
1. New
Definition: Primes are a special class of odd
numbers divisible only by themselves and 1.
And now let's consider the number 2. Let's single it out for some
abuse.
The number 2 is not the same class of prime. It is not as prime as the
other prime numbers.
Why?
Because most prime numbers, that is to say numbers only divisible by
themselves and 1, contain many more whole numbers. For example
the number 61 has 59 other whole numbers in it besides 1 and 61.
The number 2 has none.
When shopping for a nice juicy prime number, I look for fat numbers
with a lot of whole numbers in the middle. The number 2 is just a
skinny, bony little number. Or perhaps 2 is a more efficient
prime number.
Is it a more efficient prime, meeting the standards of being prime but
with zero calories, short and to the point? Is it more efficient,
or merely a more convenient
prime? Or even a fake
prime?
The math crank speaks:
I declare the number 2 to be a skinny prime. I declare the others
to be fat primes. 2 is only prime because there are no other numbers
around. Kind of like most prime real estate.
Fake prime is a little harsh, but 2 has something going against its
reputation. It has no whole numbers inside it's allegedly prime
self to attest to its greatness as a prime. In fact, to speak of
2's greatness as a prime, you have only 1, and 2. That is to say,
2 speaks highly of itself as a prime and so does the number 1. 1
only likes it because that's the only way 1 can get any more of itself.
But all those other primes have also this great line of whole numbers
to chime in. Chapters and chapters of accolades streaming in, the
bigger a prime number gets.
And the number 2 speaking for itself never convinces anybody. 2
is just pompous. 2 is arrogant. And number 1? Number
1! Mister Identity. No references. No one can take
him seriously. The first number and the first prime number
speaking for each other? Bring me the barf bag.
Back to the issue of Goldbach's Conjecture: Any two (prime therefore)
odd numbers, when added, make an even number. 2 says it makes
even numbers. I say "Shaddap. You were even already." Let's
continue assigning subjective adjectives to numbers. Odd numbers
are active. Even numbers are inert. Each odd number has --
count it -- ONE extra electron. If it passes that electron to an
even number, that even number becomes unstable. It becomes
odd. Like that three-eyed neighbor of yours with one two many
tuna casseroles.
But slap two of those odd numbers together and they resolve their
oddness. It's like civil marriage. They stabilize. Key
point: They each had ONE (1) extra, and when they bonded, the
extra 1's formed a 2, and the 2 is what made them even.
So, folks, it appears that 1 and 2 are old hucksters running the same
game all the way through the whole number series. It is always
they who are responsible for making a number odd or even. Are
they experts at it, or are
they a sideshow act, amusing as a variety show, but not worth watching
alone? Headliners, but not a main act?
Folks, I am not impressed by 1 and 2. 3 impresses me. 3 is composed of 1 and 2. 3 is
odd. 3 is prime. 3 is the first prime number with a
character witness. 1 and 2 as points can't even make a plane. How
can they make a prime? I ask you.
