Factoring large composite numbers

Let us take an integer which we wish to factor: x.
Now let y = the smallest factor greater than x, where y - x is a square
number.
Let y - x = z
Then, x = (sqrt(y) - sqrt(z))(sqrt(y) + sqrt(z))

For example:

Let x = 15
Let y = 16
y - x = 1 = z
sqrt(z) = +1 or -1
x = (4 - 1)(4 + 1)
   = 3 * 5

Does this hold much promise or is this a dead end?

Please be aware that I am only 15 years old, but I am extremely
interested in cryptography and factorising large numbers.
Received on Mon May 1 01:54:00 2006