Are modern processors safe from backdoor?
If you engage your tin-foil beanie hat and look at currently commercially available technology - basically no.

Given the fact that you could fabricate, on a microscopic sliver of silicon, a CPU with storage &amp; some sort of comms (wireless, NFC, waggling a spare pin, superimposing a comms signal as low-level noise on a pin, whatever) which would presumably only ever become active on command, then I don't really see that you can consider anything bigger than a grain of sand to be 100% NSA-proof. Possibly not even the grain of sand, depending on the fit of your beanie.

I'm half way through reading "Spycraft" by Robert Wallace &amp; H. Keith Melton (highly recommended) and the stuff they were doing and building in the 1960s and '70s is still quite impressive even now. Compared to commercially-available stuff of the time, it's astounding. So, extrapolate that level of tech to modern standards, and basically they could put anything anywhere.

Likewise backdoors - hell, it's all over the place that they've got backdoors in all sorts.

A better question to ask is does it matter? or maybe should I worry about it? or even would they bother?

Frankly, people worry about the wrong stuff. Before this Snowden stuff broke, people were worrying about a bored police employee being able to watch them via CCTV scratching their arse on the high street, or ANPR cameras being a bit too efficient at catching them speeding. No-one (normal) was wondering if the interwebs were secure, or their iPhone, or whatever.

So, while I'm sure they could do something like this, I'm fairly sure it's not worth their while doing it, or your while worrying about it.

Look out for the little black helicopters.