http://dictionary.reference.com/search?q=prim
prim adj. prim·mer, prim·mest
Precise or proper to the point of affectation; excessively decorous.
Strait-laced; prudish.
Neat and trim: a prim hedgerow.
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http://www.m-w.com/cgi-bin/dictionary
Main Entry: prim
Function: adjective
Inflected Form(s): prim·mer; prim·mest
1 a : stiffly formal and proper : DECOROUS
b : PRUDISH
2 : NEAT, TRIM <prim hedges>
- prim·ly adverb
- prim·ness noun
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Entry Word: prim
Function: adjective
Text: 1 excessively concerned with what one regards as proper or right <a prim woman, easily shocked by vulgar language>
Synonyms bluenosed, genteel, missish, precise, prig, priggish, prissy, proper, prudish, puritanical, straitlaced, stuffy, tight-laced, Victorian; GENTEEL 3
Related Word correct, nice, precise; decorous; rigid, stiff, wooden; ceremonial, ceremonious, conventional, formal, straight
Idioms prim and proper
Contrasted Words lax, loose, slack; easy, easygoing, free
2
Synonyms NEAT 2, chipper, orderly, shipshape, snug, spick-and-span, tidy, trim, uncluttered, well-groomed
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I don't think this is a super common word.