Galois Table Explorer
Every Galois table of GF(p²) for the first thousand primes, drawn on demand: step through the tables, compare each with its twin, and watch Arnold's and the Morgan Method measure how randomly the powers fall.
Tables
Point at a cell to see its exponent, the cell opposite it about the centre, and where the twin keeps it.
Close up
Arnold and Morgan on this table
Each method counts the \(N\) values below \(m\) inside its region of \(G\) cells and reports \(\lvert N/m - G/z\rvert\), with \(z = p^2\); closer to zero looks more evenly spread. Arnold's region is the first columns; the Morgan region lies between the upper arms of the diagonals.
Every table of this prime
As \(p\) grows
Arnold conjectures that \(N/m \to G/z\) as \(p \to \infty\). Here are both methods' averages for each of the first thousand primes (logarithmic axes); select a point to open that prime.
Keys: ← → previous and next table, [ ] previous and next prime, r a random table. The page computes every table in your browser; the per-prime statistics were computed once, by explore/tools/precompute.mjs.