'antiprime' is formed in modern English by combining the prefix 'anti-' (from Greek 'anti-', meaning 'against' or 'opposite') with 'prime' (from Latin 'primus', meaning 'first').

'anti-' entered English from Greek via Latin and French, and 'prime' entered English from Old French and Latin; combining 'anti-' + 'prime' as a compound produced the English term 'antiprime' used in mathematical contexts.

Initially the components simply conveyed 'against' or 'opposite of' 'prime' (i.e., not prime); over time in mathematics the compound came to be used specifically for numbers notable for having many divisors (highly composite numbers).