I looked at A115401, the record gaps between primes 3 apart, and it turns out that the gap of 112 between 35617 and 35729 is very big. The sequence starts out smoothly. After the initial 5, every even number from 8 to 36 is in the sequence. There are not many even numbers missing up to 68. Then, it jumps to 78, 84, and a really big leap to 112. That corresponds to the 35617, 35729 gap. It is an enormous prime gap!
