Melt-blown nonwoven fabric, filter, and method of producing melt-blown nonwoven fabric

A method of producing a melt-blown nonwoven fabric, the method comprising:

• forming fibers by spinning a molten thermoplastic resin, pumped to a die for melt-blowing, from a nozzle in which a plurality of small pores are arranged in a row, and by drawing and thinning by high-temperature, high-speed air jetted from slits provided in such a manner as to sandwich the row of the small pores;
• and
• depositing the fibers on a moving collection plate to form a melt-blown nonwoven fabric, wherein:
• the thermoplastic resin is a propylenic polymer that shows at least one peak top at a position of a molecular weight of 20,000 or higher and at least one peak top at a position of a molecular weight of less than 20,000 in a discharge curve obtained by gel permeation chromatography, that has an intrinsic viscosity [q] of from 0.35 dl/g to 0.50 dl/g, and
• in the forming the fibers, a cooled fluid of 30° C. or lower is fed from both sides of an outlet portion of the slits from which the high-temperature, high-speed air is jetted, via an attachment for introducing a cooled fluid for cooling spun thermoplastic resin fibers attached to a tip of the die for melt-blowing without any gap, from a horizontal direction along a nozzle surface, and the spun thermoplastic resin fibers are cooled.