A375095 Primes p such that the difference between the average of the next 2 primes after p and p sets a new record.
2, 3, 5, 7, 19, 31, 47, 83, 109, 113, 199, 523, 887, 1129, 1327, 5591, 9551, 15683, 19609, 31397, 155921, 188029, 338033, 360653, 370261, 492113, 1349533, 1357201, 1671781, 2010733, 4652353, 15203977, 17051707, 20831323, 47326693, 90438133, 164710681, 189695659
Offset: 1