Abstract. For each k ≥ 1 and corresponding hexagonal number h(k) = 3k(k + 1)+ 1, we introduce m(k) = max{(k − 1)!/2, 1} packings of h(k) equal disks inside a circle which we call the curved hexagonal packings. The curved hexagonal packing of 7 disks (k = 1, m(1) = 1) is well known and one of the 19 disks (k = 2, m(2) = 1) has been previously conjectured to be optimal. New curved hexagonal packi...