Prime number test

[Gekkey]

Alright. I am here to ask a question. I don't know if this belongs here or not.
I am using python and am on problem #10.
My program was going incredibly slow until I changed it from:

Code: Select all

for i in range(3, 2000000, 2):
        for i in range(2, x, 2):

to:

Code: Select all

for i in range(3, 2000000, 2):
        for i in range(2, x**0.5+1, 2):

I had seen that on other people's prime tests.
My question is: Why does this work?

[TripleM]

Suppose j is a factor of i. Then so is i/j. Can both j and i/j be more than sqrt(i)?