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Best Possible Densities of Dickson m-Tuples, as a Consequence of Zhang–Maynard–Tao
Abstract
We determine for what proportion of integers h one now knows that there are infinitely many prime pairs p, p + h as a consequence of the Zhang-Maynard- Tao theorem. We consider the natural generalization of this to k-tuples of integers, and we determine the limit of what can be deduced assuming only the Zhang- Maynard-Tao theorem.
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