I don't see how the birthday paradox applies. If you pick a random IP under 127.0.0.0/8, then on average a website searching will take 1/2 of time required to

I don't see how the birthday paradox applies. If you pick a random IP under 127.0.0.0/8, then on average a website searching will take 1/2 of time required to check every IP sequentially.