A prime gap is the difference between successive prime numbers; it constitutes a first occurrence when no preceding gap has an equal value. A first occurrence prime gap is maximal if the gap strictly exceeds all preceding gaps.

The merit $M$ of a prime gap of measure $g$ following the prime $p$_{1} is defined as $M=g/ln(p$_{1}). It is the ratio of the measure of the gap to the “average” measure of gaps near that point; as a consequence of the Prime Number Theorem, the average difference between consecutive primes near $x$ is approximately $ln(x)$.

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