No reply from the professor after the follow up email There is a PhD position at a university. I have sent an email and also a follow-up email (after one week from my first email) to the corresponding professor and I haven't got any reply yet (it has been 4 days from the follow up email!).

somewhere at the personal webpage of the professor it is stated that to apply or if you are interested to postdoc please first email your CV to Prof. X. On the other hand, the "Apply online" button in the open position list is active. What should I do now? send another email to the professor?
My answer will be general -- not specific to the particular institution you want to apply to.


You could contact the department and ask, "I sent my CV to Prof. X, as suggested at the application instructions page (provide link), on [date], but have not heard back yet.  May I go ahead and submit my application, or do I need to wait for a response from the professor?"
Note that four days is not very long.  Depending on the application deadline, you may want to give this a bit more patience.
You have submitted your CV as instructed; unless the instructions say you must hear back from the professor before submitting your application, I suppose you could go ahead and submit your application.