I've applied to a software development company for a programming position. I'm communicating directly with an employee, specifically a project manager, not a recruiter.

I made it through a phone interview and was given a take-home project to work on. I completed the project and submitted it, via email, to the person who I have been communicating with. It has been a week since I submitted it and have not heard back from the person.

Now, assuming he's not intentionally ignoring me, I think he's just busy / forgetting to respond to me. I've been communicating with him for quite a while, and this is not the first time that he has just been too busy to respond. I'm pretty far in the interview process and I really want to work for this company, so I don't want to just give up and let this opportunity pass by.

How can I politely email him and ask if he had the chance to review my take-home project? I put a lot of hours into it, and even more months of initial preparation for the position before applying. I'd really like to hear back even if it's that my project was not strong enough.

Should I just directly ask if he's looked at it? Is there maybe a more indirect way of bringing it up, like submitting a "revised" version? I just don't want to annoy him. but I'd really like to hear back from him.