Weird, I just read about this exact example yesterday in the "music of primes" by Markus De Sautoy. I'm not sure though if it was the German Siegel or the Norwegian guy (Sebel or something) who also end up to Princeton to figure it out, or maybe it was known already by Euler's time :-)
I first read it a few years back in Excursion's in Number Theory [0]. Super approachable (and short!), I read it in high school with only a little bit of calculus knowledge.
Neat proof indeed.