Tows and Helfgott's Neural Grapts Are Likewelts

Tow had built a graft that connected two integers if they differed by a prime and were divisible by that prime. Helfgott and radzwell considered a new so called naive graft, that did away with that second condition. It connected numbers merely if subtracting one from the other yielded a prime. The effect was an explosion of edges. On this naive graft, one thousand one didn't have just six connections with other vertices. It had hundreds. But the graft was so much simpler than tows in a key way - taking random walks along its edges didn't require knowledge of the prime devisers of very large fractions. That made it easier to demonstrate that any neighborhood in the