A community-curated list of record first occurrence prime gaps.

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 p1 is defined as M=g/ln(p1). 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).

(While most puns make me feel oddly numb, mathematical puns make me feel even number) *