Over-primed?

I used a recipe kit for a 5-gallon batch, and didn't realize until I was done bottling, that we only got 37 12oz (I think, will recount next time I'm downstairs) bottles out of it. I used the entire 3/4 cup of corn sugar provided, which I now realize is probably too much for the less-than-5-gallons I ended up with.

Should I be concerned about bottle bombs with this mis-measurement? They have been in bottles 1 week. Do I need to open and re-cap them? If so, how do I know when to do this? Should I open one at 2 weeks to see how they are carbing? Will they just be over-carbed but safe?

Thanks
Aaron

Ok here's what I could come up with.

Normal batch is 640oz of beer, you made 444oz, or about 70 percent the volume you thought you did.

So by my math you would have added 30 percent more sugar than intended, so 6oz in a 444oz batch is like having 7.8 oz in a 640 gallon batch.

6oz of sugar would yield a carb level of 2.27 in 5 gallons of beer, a good number. 7.8oz would result in approx 2.9 volumes.

It will be carbed like a hefe more than an ale. I've read the theoretical limit on 12oz bottles is 3 volumes. Be sure to ferment these at 68 degrees, not warmer or you'll end up with bombs. Chill em for 48h before opening and be careful for the first few.

Thanks for the feedback. They are in the basement, which stays well below 70F so it sounds like I should be alright with a bit of caution & care. Anybody else care to offer an opinion, based on calculations or pure experience?

Thanks
Aaron

To follow-up on this for future readers, I have not had any problems with exploding bottles. After ~3 weeks the carbonation was adequate to begin drinking these. As time went on, the carbonation level rose a bit more making them noticeably (but not critically) over-carbed. They pour fine (no excessive head or foam) but they have kind of over-sized CO2 bubbles (like cheap seltzer water) instead of smaller foamy bubbles like most beer. No gushers either.