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There are a few different methods being used for current gap finding efforts:

• Exhaustive search.  This is looking for true record gaps, which means it started at 2 and went up from there.  It's intensely computationally expensive.  Tomás Oliveira e Silva ran a distributed project from 2005 to 2012 that got to 4e18 using years of work on hundreds of cores.  Interestingly, the computational result was used in Helfgott's 2013 proof of the Odd Goldbach Conjecture.  Recently the PGS team at mersenneforum have used a different method to extend this and after about 9 months have brought this to 10e18.  The number of records per computational effort is very small, however these are true Minimal Gaps -- once found the record is permanent, as no earlier gaps of that size exist.

• Gapcoin.  For relatively small P1 values (84-347 digits), choose a random small range, sieve out small multiples, then run Fermat tests to find gaps.  While each step is efficient and fast, it's rather inefficient at finding record gaps.  It's basically rapidly throwing darts while blindfolded and being spun around -- the only way to get more darts in the target is to throw faster.

• Primorial methods.  Gaps are far more common at multiples of primorials without some small divisors, e.g. numbers of the form N * p# / k with k a small square free number.  So if one looks at increasing values of N * 191#/30, for instance, using efficient methods for finding the previous and next primes around that point, one can find record gaps many times times faster than the gapcoin method.  That is the method used by most other searchers and is what holds all but 3 of the highest merits (those three being from the exhaustive search).  There are some minor variations -- Hans Rosenthal in 2017 did searches with a fixed large N and instead varied k.  Using the dart analogy from before, this is throwing darts while aiming at the target.  The darts are thrown a lot slower, but since they're all thrown in the direction of the target rather than randomly around the room, more of them result in high results.

There may be other methods.  I don't know how Helmut Spielauer finds results (he holds most of the records from 1400-3000), and while searchers like Michiel Jansen use the N*p#/k form, it's not known what software or algorithm is used.