The First Check Number field is used in conjunction with the check generation process.  This field is not used for Search filtering purposes, but rather as input to the check generation process.

This value will default to the "Last Check # Used" plus 1 from the profile of the selected Bank Account (as defined on the Admin >> Setup >> Bank Accounts screen).

When the Print Checks option is checked, this field is required.  When the Print Checks option is not checked, this field is disabled.