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We define a group stucture on the primitive integer points (A, B, C) of the algebraic variety Q 0 (B, C) = A n , where Q 0 is the principal binary quadratic form of fundamental discriminant ∆ and n ≥ 2 is fixed. A surjective homomorphism is given from this group to the n-torsion subgroup of the narrow ideal class group of the quadratic number field Q( √ ∆).

Abstract. Pell conics are used to write a Proth-Riesel twin-primality test. We discuss easy-to-find primality certificates for integers of the form m n h ± 1. The known primality test for 3 n h ± 1 is associated with X 2 + 3Y 2 = 4.

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