5

You know prime numbers, right?  A prime number is a number that only has one and itself as factors.  Thus, the first couple of primes are 2 (the only even prime), 3, 5, 7, 11, 13, 17, 19, 23, 29, …

That’s what most of us learned at some point in our early math educations. 

But I just found out something so freakishly cool, it gave me goose bumps.

Note: It may not give you goose bumps.  It probably won’t give you goose bumps.

Take that number 5.  It isn’t really a prime.

No?

Why not?

What other numbers, besides 1 and 5, multiplied together, yield 5?

Well, two complex numbers multiplied together can result in 5.

A complex number is a real number plus an imaginary number.  An imaginary number is the square root of minus-one.  It is represented by the letter i.  Trust me, these types of numbers exist, are fully accepted in the mathematical community, and actually have direct applications in the physical world.

Ready?

… drum roll …

5 = (1 + 2i) (1 – 2i)

To multiply this out, multiply the first two numbers, the last two numbers and the inner-outer and outer-inner numbers.  When we do this, we get:

1 + 2i - 2i + 4

[That last two numbers multiplies out to minus-4 times minus-1, which is 4.]

[The middle terms cancel out.]

The result is:

1 + 4

Which equals

5.

Ergo, 5 is not a prime number, because it is the product of

(1 + 2i)

and

(1 – 2i)

Right?