A premix burner for producing an ignitable fuel/air mixture has a swirl generator with at least two burner shells (B) which complement one another to form a throughflow body, which in each case have a first burner shell section (1) with a partial cone shape and together enclose an axially conically widening swirl space and which mutually define, in the axial cone longitudinal direction, tangential air inlet slots (LS), through which the combustion feed air (L) passes into the swirl space, in which an axially spreading swirl flow forms, and includes fuel feeds which are arranged at least in sections along the tangentially running air inlet slots (LS). A second burner shell section (8) curved in opposition to the first burner shell section (1), in each case designed in a partial cone shape, is added flush to the first burner shell section (1), a third burner shell section (9) adjoins the second burner shell section (8) flush, the third burner shell section (9) having a curvature tangentially adapted to the second burner shell section (8), and the third burner shell section (9) defines, on the one side in each case, one of the tangential air inlet slots (LS) and provides a leading edge (12) serving for the combustion feed air (L).