type of evergreen shrub, 1540s, of unknown origin. Early forms primet, primprint perhaps suggest some connection with the word prime.  prime (adj.) 
late 14c., "first in order," from Latin primus "first, the first, first part," figuratively "chief, principal; excellent, distinguished, noble" (source also of Italian and Spanish primo), from pre-Italic *prismos, superlative of PIE *preis- "before," from root *per- "beyond, forward, through" (see per). Could be in reference to Petunia being the first born of the two Evans sisters.