When n=3, a big gap seems like 35617, 35671, 35677, 35729. There is a gap of 54 between 35617 and 35671, which is big for numbers of that size. After the gap of 6 between 35671 and 35677, there is another big gap of 52 between 35677 and 35729. Therefore, the 3gap between 35617 and 35729 is a surprisingly large prime gap.
