Elliptic pseudoprime

Template:Short description 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 $\mathbb{Q}\left(\sqrt{-d}\right)$, 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 Template:Nowrap.

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

$X/\exp ((1/3)\log X\log \log \log X/\log \log X).$

References

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External links

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