A timepiece mainspring including, in the manufactured state, an eye and a portion formed of coils with an outer coil of radius R, the eye and the portion formed of coils being connected by a neck portion having substantially zero curvature, the timepiece mainspring wherein the neck portion has a length LC comprised between 1.5 and 10 times, and preferably between 2 and 8 times, the radius R. The mainspring having this specific geometry reduces the risk of premature breakage during use, typically for an application with a k factor lower than 10.