Elliptic pseudoprime explained

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

Q ( \sqrt{ - d} ) , 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 .

The number of elliptic pseudoprimes less than X is bounded above, for large X, by

X / \exp(( 1 / 3 ) log X logloglog X / loglog X) .

References

• Gordon . Daniel M. . Pomerance . Carl . The distribution of Lucas and elliptic pseudoprimes . . 57 . 196 . 825–838 . 1991 . 0774.11074 . 10.2307/2938720. 2938720 . free .