Drill pipe having concave wrenching recesses

A drill pipe has a central axis and comprises a first end and a second end with a portion of the second end being substantially triangular in the lateral cross-section and having three faces. At least one concave wrench recess is located in each of the three faces of the substantially triangular portion of the second end. Each of the recesses has a surface with an axially extending center line. The center line is located a predetermined distance from the central axis, with this predetermined distance being less than or equal to the distance from the central axis of all other axial lines on the surface of the recess. Each of the recesses may be comprised of two adjoining planes having exterior surfaces, the cross-section of the two adjoining planes forming an angle of less than 180 degrees as measured from the exterior surfaces of the two adjoining planes. Alternatively, the recesses can be comprised of three adjoining planes. Finally, the recesses may be comprised of an arcuate segment.