Prime k-tuple conjecture
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There are infinitely many prime k-tuples for every admissible tuple.
Generalization of the Twin prime conjecture.
As of 2023, there was no specific admissible tuple for which it had been proven that there infinite of, only bounds of type:
But these do not specify which specific tuple, e.g. Yitang Zhang's theorem.
there are infinitely 2-tuple instances with at most a finite bound