Spectral test
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The test that ranks the generators
Every linear generator's output lies on a family of parallel planes. Which generator is better is decided by how far apart those planes are, and that distance is the length of the shortest whole-number vector the modulus annihilates — a quantity that can be computed exactly rather than estimated by testing.
Birthdays spaced too evenly
Scatter n birthdays through a year of k days, sort them, and count how many of the gaps between neighbours repeat an earlier gap. For random birthdays the count is close to a Poisson variable with mean n³/4k. A linear congruential generator with m states, read in pairs, matches that law until the grid has as many cells as the generator has states, and then leaves it at once: at sixteen times as many cells, every run of the spacings count rejects it. The sample that catches it is about five times the cube root of the period — 8,192 outputs for a 32-bit generator, thirteen million for a 64-bit one — and the same states, scrambled before they are read, pass.
Named alongside it
The objects these essays reach for when they reach for this one.
LatticePseudorandomnessBirthday problemCollisionCounting two waysDimensionModular arithmeticPeriodRandomnessShortest vectorUniform distribution