As the number of primaries used in an imaging system increases, so does the cost of computing the resulting color gamut. While for three or even four primaries it is possible to use exhaustive techniques to generate a relatively small number of samples that provide sufficient gamut boundary information, taking the same approach with devices using a larger number of primaries (e.g. 6+) leads to a combinatorial explosion. To address this issue while providing accurate information about the color gamut of a multi– primary device, the present paper describes the PSS primary space sampling algorithm that reduces gamut computation time from centuries to seconds.