The Collaborative International Dictionary of English v.0.48:

Primness \Prim"ness\, n.
   The quality or state of being prim; affected formality or
   niceness; preciseness; stiffness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

primness
    n 1: excessive or affected modesty [syn: primness,
         prudishness, prudery, Grundyism]
    2: exaggerated and arrogant properness [syn: priggishness,
       primness]

Moby Thesaurus II by Grady Ward, 1.0:

41 Moby Thesaurus words for "primness":
   Quakerishness, buckram, censoriousness, ceremonial,
   ceremoniousness, ceremony, demureness, demurity, dignity,
   extrinsicality, false modesty, form, formality, formalization,
   gravity, hideboundness, impersonality, mauvaise honte, narrowness,
   overmodesty, pomp, pomposity, priggishness, prudery, prudishness,
   puritanicalness, rigidness, ritual, rituality, sanctimoniousness,
   sanctimony, smugness, solemnity, starchiness, stiff-neckedness,
   stiffness, stiltedness, straitlacedness, stuffiness, stylization,
   weight