Should I inform my professor of a very recent paper vaguely related to his research? I'm currently an undergrad student and have found a recent paper, published in Nature a few days ago, that represents a huge breakthrough in its field (I'm active in that area, so I'm aware of it), but has barely been reported elsewhere.

One of my professors is doing research in a related, but not the same area. I was thinking of sending him a short email along the lines of "It seemed like this might be of interest to you, so just for your information: There has been a breakthrough in [area] recently, published at [link to Nature online], in which ..." and one or two sentences about the content.

It is nothing that requires a lot of thought to understand, and the fact that it happened at all is more important than the details. One can easily understand most of it from the abstract.

Would such an email generally be considered more of an annoyance, or acceptable?

Update:
Thank you all for your helpful answers and also the many interesting comments. I have sent him an email and received a short reply.
Yes, send it. We all like to get links to papers we might have missed. I would leave out the "breakthrough" part. He may have seen it (or even reviewed it), but there is no harm in sending it along to either him or his entire research group.