A -matching in a hypergraph is a set of edges such that no two of these edges intersect. The anti-Ramsey number of a -matching in a complete -uniform hypergraph on vertices, denoted by , is the smallest integer such that in any coloring of the edges of with exactly colors, there is a -matching whose edges have distinct colors. The Turán number, denoted by , is the the maximum number of edges in an -uniform hypergraph on vertices with no -matching. For , we conjecture that if , then . Also, if , then , where is a constant dependent on . We prove this conjecture for , and sufficiently large , as well as provide upper and lower bounds.