Patchy coverage in the Prime Gap List
Some trivial SQL exploration of the prime gap list records SQL file available from the Prime Gap List repository reveals interesting differences in depth of exploration of prime digit length ranges. Below is a short list of a range of prime digit lengths covering the shift ranges from 16 to 128 and a COUNT of the first known occurrence gaps recorded for that range:
82: 100, 83:010, 84:012, 85:264, 86:04, 87:053, 88:001, 89:003,
90: 001, 91:008, 92:000, 93:006, 94:014, 95:018, 96:010, 97:206,
98: 005, 99:016, 100:016, 101:002, 102:012, 103:007, 104:013, 105:015,
106: 121, 107:016, 108:010, 109:015, 110:021, 111:012, 112:034, 113:026,
114: 049, 115:023, 116:142
So, while there have been 100 record gaps submitted for the range of primes with length 82, only one record has been submitted for the range of primes with length 88 and for the range of primes with length 90. Interestingly, no records at all have been discovered and submitted for the range of primes of length 92.
There is an obvious correspondence between the number of records discovered/submitted and the popular/default Gapcoin shift settings - 16 was the original default setting for GapMiner, later increased to 25 and then there are the popular multiples of 16: 32, 64, 96 and 128:
