Two lattice points (x, y) and (x', y') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that (x' - x, y' - y) = 1, where (m, n) denotes the greatest common divisor. The plots above show the first few points visible from the origin. If a lattice point is selected at random in two dimensions, the probability that it is visible from the origin is 6/π^2. This is also the probability that two integers picked at random are relatively prime. If a lattice point is picked at random in n dimensions, the probability that it is visible from the origin is 1/ζ(n), where ζ(n) is the Riemann zeta function.
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