at least
Synonym discussion
Sense: idiom/1
All four expressions set a lower limit, but they differ in tone and typical use. 'At least' is the most natural and frequent choice in everyday speech and writing — it fits casual conversation, business emails, and academic work equally well. 'No less than' carries a shade of surprise or emphasis, often appearing before surprisingly large numbers: 'The painting sold for no less than two million dollars.' 'A minimum of' sounds more official and precise; you will see it on forms, contracts, and instructions: 'A minimum of three references is required.' 'At the minimum' is close to 'a minimum of' but feels slightly more conversational. 'Not under' is the least common and mainly used with ages or prices in formal notices: 'Not under 18 years of age.' For most situations, 'at least' is the right choice — the others add nuance when you need it.
Etymology
First known use
12th century
12th century, in the meaning defined at sense 1