Part III · Interactive
Pour two primes into a bucket — just right, every time.
A prime is a bucket you can't fill with equal cups — every cup size overflows or underflows, so it's indivisible. Pick an even number and watch pairs of prime buckets pour together to fill it exactly: no spill, no shortfall. Each even number has its own count of pairs that work — and the count never hits zero.
Each pair pours to exactly 100
Two prime buckets tipped into one E-sized bucket. The dashed line is the brim — the water has to land exactly on it: no overflow, no underflow. Every pair below hits it, because 100 = p + q.
The 1000 buckets
Every number 1–1000 as a bucket. A prime holds its water — nothing divides it evenly, so it's “just right.” A composite leaks (dashed, empty). The two buckets used in the current pour glow green. 1 and 2 are special.
How many pairs each even number has
One bar per even number, 6 → 1000. Height = how many prime pairs fill it. Click a bar to jump there. It never touches zero — that is Goldbach, verified across all 498 of them.
minimum pairs across every even 6–1000: 1 — never 0.
The comet never touching zero is exactly Goldbach — and proving it stays up for every bar forever is the open part (see the write-up). The buckets make the mechanism vivid; they can't cross that last gap, but nothing visual can.