Record runs of consecutive primes with non-square gaps: 2,0, 3,2, 23,3, 47,4, 131,6, 233,8, 503,16, 4157,32, 19433,34, 213023,45, 2441237,52, 3239393,56, 6638393,60, 7524233,66, 8528687,68, 10778687,76, 17922347,84, 192199181,85, 584054411,91, 609488423,97, 984197369,108, More terms? -- Zak Seidov