Obtain passport numbers issued between 1925 and the present with a notarized written request sent to the Department of State Passport Services in Washington. Currently, it is not possible for U.S. Citizens to obtain a passport number based on their name alone.
Under the Privacy Act, it is possible to obtain copies of passport records in your own name as well as those of your children if they are classed as minors. Requests for this information must be in the form of a clearly printed or typed letter containing full birth name and subsequent name changes, date of birth, estimated date the passport was issued and contact details. Valid photographic identification is required, and additional passport numbers assigned to you in the past may help to discover your most recent number.
Passport numbers expire with the passport and subsequent passports issued contain a different passport number. Therefore, if an old passport is in your possession, but it is not your most recent, it does not have the same number but it can be used to identify other numbers assigned to you.