A passport number is one way the United States can identify you for security purposes if you have lost your physical passport. The only way to get this number is off of your passport. There is no way to contact an office to get the number without ID. This is why it is important to keep a copy of your passport in a safe place in case you misplace the item.
Open your passport to the first page. On the inside cover you will find all your information. The passport number is located on the top right corner under "Passport No."
Review the copies of your passport that is kept in your files. You should always keep a copy of this document just in case you misplace the item. With a copy you can at least access the information while waiting for a replacement. You just need to copy the inside cover of the document.
Apply for a new passport to get your passport number. Since you cannot get the number in person or over the phone, fill out an application to replace your lost passport. You must include the fee and proper identification. You can replace a passport through the mail or in person at passport agency. The new passport will arrive in the mail.