'non-prime' originates from English as a compound of the prefix 'non-' and the adjective 'prime'. The prefix 'non-' ultimately comes from Latin 'non' meaning 'not', and 'prime' comes from Latin 'primus' meaning 'first'.

'prime' came from Latin 'primus' → Old French/Latin-influenced forms → Middle English 'prime'. The negative prefix 'non-' was used in English to form opposites and compounds (e.g., nonconformist), producing compounds like 'non-prime' in modern English usage.

Initially 'prime' meant 'first' or 'of first importance'; the compound 'non-prime' simply meant 'not first' or 'not primary'. Over time it developed specialized senses, e.g., in mathematics ('not a prime number'), broadcasting ('outside prime time'), and finance ('not prime credit').