Suppose a given prime gap $ k $ where $ k $ is an even positive integer occurs infinitely often, that is, one has $ p_{n+1}-p_{n}=k $ for infinitely many values of $ n $. Does it suffice to entail that the density of such primes $ p_{n} $ below $ x $ is $ \asymp\dfrac{x}{\ln^{2}x} $?
2026-04-01 13:06:42.1775048802
Frequency of a given prime gap knowing it occurs infinitely often
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