The vast majority of cell phone numbers are not listed in free phone number directories. This is because cell phone numbers are maintained and distributed by individual cell service providers rather than an interconnected network of phone companies the way land line numbers are.
There is one directory that offers free access to a database of cell number at select times. The National Cellular Directory occasionally hosts happy hour events, at which time all searches for cell numbers made using the company's website are free. Users who want to take advantage of this must register with the National Cellular Directory and keep an eye on social media to see when the next happy hour event is being held.