The Solanum tuberosum L. Phureja Group consists of potato landraces widely grown in the Andes from western Venezuela to central Bolivia, and forms an important breeding stock due to their excellent culinary properties and other traits for developing modern varieties. They have been distinguished by short-day adaptation, diploid ploidy (2n = 2x = 24), and lack of tuber dormancy. This nuclear simple sequence repeat (nSSR or microsatellite) study complements a prior random amplified polymorphic DNA (RAPD) study to explore the use of these markers to form a core collection of cultivar groups of potatoes. Like this prior RAPD study, we analyzed 128 accessions of the Phureja Group using nuclear microsatellites (nSSR). Twenty-six of the 128 accessions were invariant for 22 nSSR markers assayed. The nSSR data uncovered 25 unexpected triploid and tetraploid accessions. Chromosome counts of the 102 accessions confirmed these nSSR results and highlighted seven more triploids or tetraploids. Thus, these nSSR markers (except 1) are good indicators of ploidy for diploid potatoes in 92% of the cases. The nSSR and RAPD results: (1) were highly discordant for the remaining 70 accessions that were diploid and variable in nSSR, (2) show the utility of nSSRs to effectively uncover many ploidy variants in cultivated potato, (3) support the use of a cultivar-group (rather than a species) classification of cultivated potato, (4) fail to support a relationship between genetic distance and geographic distance, (5) question the use of any single type of molecular marker to construct core collections.