http://qs321.pair.com?node_id=203853


in reply to Re: YAPNC: Yet another prime number checker?
in thread YAPNC: Yet another prime number checker?

You can stop at sqrt($input).

Example:
The divisors of 100 are:
1, 2, 4, 5, 10, 20, 25, 50, 100. They come in pairs as follows:

1*100 = 100 2*50 = 100 4* 25= 100 5*20 = 100 10*10 =100 20*5= 100
and so on. So at 10 which is sqrt(10) you are at the point where the second factor is smaller than the first and you have already tested for this pair.