Prioritizing Energy Efficient Renewables Act of 2013 - Amends the Internal Revenue Code to: (1) make permanent the tax credit for producing electricity from wind, geothermal and solar energy, hydropower, and marine and hydrokinetic renewable energy facilities; (2) repeal the tax deduction for intangible drilling and development costs for oil and gas wells; (3) repeal the tax deduction for income attributable to the production, refining, transportation, or distribution of oil, natural gas, or any primary product thereof; and (4) repeal the percentage depletion allowance for oil and gas wells.