Follow up email in 2 weeks - PhD application - a good idea? I had written to a well know professor in my field of study regarding a possible PhD position. He responded and asked for references. I was dumb enough to respond to this mail after 4 days. It has been two weeks since the last email and I never heard from the professor. 


Is it a good idea to send a follow up email?
Do you think the delay in responding to his mail would have spoiled my chances?
No, the delay didn't spoil your chances, and no, don't write a followup.

The prof wasn't waiting for your reply, and didn't expect it to come the next day. If he is "well known", he may get dozens of applications every week, plus hundreds of other emails. He likely didn't notice the delay, but just processed the daily flood of messages.

Even if he did remember when your first mail came, he knows that compiling a good application with references takes time. You usually have to write a reference yourself and find a professor who knows you at least by sight to sign it. You could have been out of town for a job interview, ill, etc., there are a million very legitimate reasons why you didn't have it ready by the next day. 

If he actually has an open position in which you might've fit, he has surely checked your references, and didn't like them. If not, there is little you, or he, could do.