2013's breakthrough (Yitang Zhang, later sharpened by the Polymath collaborative project to a gap of 246) proved infinitely many prime pairs exist within SOME bounded gap, but closing that gap all the way down to exactly two, the original conjecture, remains open.
What would resolve this A proof narrowing the proven bounded gap (currently 246) all the way to 2, or a fundamentally different argument establishing the gap-2 case directly.
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