Honestly, when we're being realistic:

-the fact that he never managed to set his wristwatch auto beacon, is an indication that there may have been a severe crash in which case he never had a chance.

-the fact that he didn't manage a beacon afterwards could indicate he wasn't capable of doing so, which would extremely limit his chances of surviving 3 weeks

-if he simply can't make a beacon, at least one that is noticed, and he's not significantly wounded, he either couldn't sustain resources in which case he'd have died soon, or he could have managed to find a sustainable way of surviving in which case 3 weeks isn't that long.

So in short, I don't think chances of survival are high, but if he survived say the first 10 days, 3 weeks or a bit more isn't the largest problem. If he was still alive by that time, he knows how to pull it longer too. Certainly Fossett.

I haven't given up all hope, but I don't think chances of finding him alive are high.

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