Lucas–Lehmer–Riesel test

In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N = k ⋅ 2ⁿ − 1 with odd k < 2ⁿ. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form. For numbers of the form N = k ⋅ 2ⁿ + 1 (Proth numbers), either application of Proth's theorem (a Las Vegas algorithm) or one of the deterministic proofs described in Brillhart–Lehmer–Selfridge 1975 (see Pocklington primality test) are used.