Notes from the workbench.

Getting up to the frontier: what analysing prime gaps actually showed

July 2026. A prime gap is a delta — the distance from one prime to the next — and deltas are how you get at a rate of change. An outsider's week-long run at the frontier of that problem, entirely through AI agents. The average miss on the nth prime fell from 1.4 million to 275, the leftover error turned out to be built from Riemann zeta zeros, and two results had been built already — once in 1970, once in May 2026. What is classical, what is now closed, and what is genuinely still open.