| Notes by Thomas R. Nicely:
No gap exceeding 1442 has been definitively established as a first occurrence; larger gaps included in these lists are instead first known occurrence prime gaps. The smallest gap whose first occurrence remains uncertain is the gap of 1208.
prime,gap
2, 1=1^2
7, 4=2^2
1831, 16=4^2
9551, 36=6^2
89689, 64=8^2
396733, 100=10^2
11981443, 144=12^2
70396393, 196=14^2
1872851947, 256=16^2
10958687879, 324=18^2
47203303159, 400=20^2
767644374817, 484=22^2
8817792098461, 576=24^2
78610833115261, 676=26^2
497687231721157, 784=28^2
2069461000669981, 900=30^2
22790428875364879, 1024=32^2
78944802602538877, 1156=34^2
2980374211158121907, 1296=36^2
18479982848279580912452968237, 1444=38^2
10338270318362067887873513954823823, 1600=40^2
5462539353768233509094313080601639583, 1764=42^2
9634432076725832064810529394509018411, 1764=44^2
24103660699017475735076387748469761375352177, 1936=46^2
1171872038536282864481405693168029955108099, (*48^2*)
169512938487733553802932479078305855585466971701227, (*50^2*)
228422210024736896126707605155690522381875250546666532046327, (*52^2*)
7229972437439469171089374324333535009566526827968927563, (*54^2*)
1263895714932859021916447978075625934206362807439043695674222113, (*56^2*)
569493611436727594340298806603382857255173440636060754222617328828425379, (*58^2*)
281376087412013738611508677824321032930454474305215907812114263492815921, (*60^2*)
680561565394793619717614472954048053005171290126070180152868857556290989645629867 (*62^2*)
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