Northamptonshire ( abbreviated Northants or N ` hants ) is a county in central England with a population of 629,676 ( 2001 census ) . Northamptonshire ( or ; archaically , the County of Northampton ; abbreviated Northants . or N\/hants ) is a landlocked county in the English East Midlands , with a population of 629,676 as at the 2001 census .