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For an elliptic curve E with complex multiplication by an order in K = Q('A-Ai), a point P of infinite order on E, and any prime p with (-d \ p) = -1, we have that (p + 1) • P = O(modp), where O is the point at infinity and calculations are done using the addition law for E. Any composite number which satisfies these conditions is called an elliptic pseudoprime. In this paper it is shown that, assuming the Generalized Riemann Hypothesis, elliptic pseudoprimes are less numerous than primes. Indoi:10.1090/s0025-5718-1989-0946604-2 fatcat:67iwr6k3gjaxrghp6xdkf7quji