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I wrote out "Every even integer >2 can be expressed as the sum of two primes" on a sheet of paper.

We'll see if staring produces a proof.

Edit: had some interesting thoughts but after 20 minutes the goldbach conjecture remains...unproven :)

I went to a talk about this a few days ago - it's interesting how much genuinely good progress has been made on the problem. Just staring at the original statement might not get you far, but internalizing and then staring at the substantial work already done might trigger a breakthrough.

Mind you, that's hard work, you might not feel inclined.

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