In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbers with complex multiplication by an order in , having equation y2 = x3 + ax + b with a, b integers, P being a point on E and n a natural number such that the Jacobi symbol (−d | n) = −1, if (n + 1)P ≡ 0 (mod n).
The number of elliptic pseudoprimes less than X is bounded above, for large X, by
- Gordon, Daniel M.; Pomerance, Carl (1991). "The distribution of Lucas and elliptic pseudoprimes". Mathematics of Computation. 57 (196): 825–838. Zbl 0774.11074. doi:10.2307/2938720.
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