Correct spelling for the English word "primemess" is [pɹˈa͡ɪmmɛs], [pɹˈaɪmmɛs], [p_ɹ_ˈaɪ_m_m_ɛ_s] (IPA phonetic alphabet).
The second quality of pickled pork, in which the barrels contain the hams and shoulders as well as the sides.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
There is no information available on the word "primemess". It is possible that it is a colloquial or slang term, a misspelling, or a made-up word without an established etymology.