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
![{\displaystyle X/\exp((1/3)\log X\log \log \log X/\log \log X)\ .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9fbce95f332d4271e04bb1fc60f5a561e562a5eb)
References
- Gordon, Daniel M.; Pomerance, Carl (1991). "The distribution of Lucas and elliptic pseudoprimes". Mathematics of Computation. 57 (196): 825–838. doi:10.2307/2938720. JSTOR 2938720. Zbl 0774.11074.
External links
- Weisstein, Eric W. "Elliptic Pseudoprime". MathWorld.
Classes of natural numbers
Powers and related numbers |
---|
|
|
|
|
|
Possessing a specific set of other numbers |
---|
|
|
Expressible via specific sums |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Mathematics portal |
![Stub icon](//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Numbers.svg/32px-Numbers.svg.png) | This article about a number is a stub. You can help Wikipedia by expanding it. |