Abstract
We prove that the sequence of gaps in the sequence of prime numbers contains infinitely many runs of three terms, with the middle term exceeding both the first and third, provided that there is at least one integer $m$ exceeding $3$, and at least one set $A$ of $2^{m-2}$ integers, with infinitely many translations of this set $n+A$ such that they contain at least $m$ primes.
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