Yeah, the root on that is indeed massive. Yes, repot up one or two sizes. Standard cactus care and full sun. This genus is, surprisingly, closely related to Ferocactus. The flowers are absolutely wonderful, big, yellow, and beautiful.

Don't expose the caudex yet, it will grow better under the soil for now. Our friend Caudex here has a magnificent old specimen with an exposed caudex. Perhaps he will share a photo ;-)

Brad

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It will get fatter faster if left buried. I have to keep my plants shaded(they look best), full sun is too intense for them.

2in diameter trunk
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5in diameter trunk
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I've had this little guy for about 6 months, hasn't budged.
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I just found this information at Henry Shaw Cactus Society. It was their "Cactus of the Month" December '08.
I found mine last year and hadn't got to know it yet so thanks for reminding me.

By Barbara Wedler

Leuchtenbergia principis is a very interesting-looking cactus. It is a monotypic genus, which means that there is only one species in the genus. It is not a large plant, as its mature height is about 24 inches, but it is quite showy, with long, blue-green tubercles and papery spines.
The tubercles are the reason for its two common names: agave cactus and prism cactus. Each half- to three-quarter-inch-wide, three-sided tubercle can be up to 6 inches long. The light-brown, papery spines grow from the blunt tips of the areoles of the tubercles. There are eight to 14 radial and one or two central spines, which are up to 6 inches long.
L. principis have a very large taproot that looks similar to a parsnip root in color and shape. The root can be 8 to 10 inches long and 3 inches in diameter.
As the plants age, lower tubercles may fall off, exposing the light-brown trunk. It has woolly axils. Lower tubercles tend to dry out and brown, especially at their tips. Upper tubercles often have a little purple at their edges.
L. principis are native to the San Louis Potosi, Hidalgo, area in north-central Mexico. The elevation there is 4,800 to 6,000 feet. The plants grow in full sun to partial shade, and experience moderate rain in summer and almost no rain in winter. As a result, they are dormant in winter and grow in the warm summer months.
In cultivation, temperatures in winter should be mildly cool, at least 50 to 60 degrees. Summer temperatures should be 75 to 85 degrees in the day and at least 60 to 65 degrees at night. A well-draining soil is needed with little or no water in winter and regular watering in summer. If leuchtenbergias do not get enough water in the growing season, the upper tubercles turn brown prematurely.
In cultivation, L. principis are usually propagated by seeds, as they rarely pup or have offsets. It has been reported that the plants can be propagated by tubercle cuttings, but this method is not common.
The flowers of Leuchtenbergia principis grow from the areoles at the ends of young tubercles. The flowers are yellow in color and are 3 to 4 inches in diameter. Plants do not bloom until they are at least 5 years old, when they bloom sporadically from spring until fall.

Thanks for all the info. I am going to repot the plant soon since is currently summer and were experiencing 95 degree days.
Thanks again