Prioritized Paycheck Protection Program Act or the P4 Act This bill authorizes new lending under the Paycheck Protection Program, established to support small businesses in response to COVID-19 (i.e., coronavirus disease 2019), for specified small businesses that have experienced a significant loss in revenue. Specifically, the bill authorizes one supplemental paycheck protection loan for a small business that (1) has no more than 100 employees, (2) operates under a sole proprietorship or as an independent contractor, or (3) is self-employed. To be eligible for a supplemental paycheck protection loan, such small business must demonstrate a loss of revenue of 50% or more and have either already expended an initial paycheck protection loan or be on pace to exhaust such loan prior to disbursal of the supplemental loan. The bill also extends the application deadline for an initial paycheck protection loan to December 31, 2020, and it authorizes loan recipients to apply for forgiveness as early as eight weeks after the loan's disbursal. The Small Business Administration must (1) issue guidance instructing lenders of paycheck protection loans to prioritize loan processing for and disbursement to underserved businesses, (2) update the loan application for paycheck protection loans to collect borrowers' demographic information, and (3) publish specified program information on its website.