Primes and subtraction · Grades 5–8 · Unsolved

Gilbreath's Conjecture

List the primes. Subtract neighbors to make a new row. Keep going. Every new row starts with 1.

The primes on top, then rows of differences. The first number of every row is 1, in orange.

Try it

2, 3, 5, 7, 11…1, 2, 2, 4…1, 0, 2…

Norman Gilbreath noticed it in 1958, doodling on a napkin.

Computers have checked hundreds of billions of rows. It has never failed.

Why do the rows fill up with 0s and 2s?

Start with a different list, like 1, 2, 4, 8, 16. Does it still work?

Detailed one-pager (PDF) History, why it’s unsolved, and more classroom ideas