Innumber theory, apseudoprime is called anelliptic pseudoprime for (E, P), whereE is anelliptic curve defined over thefield ofrational numbers withcomplex multiplication by anorder in${\displaystyle \mathbb{Q}(\sqrt{-d})}$, having equationy² = x³ + ax + b witha,bintegers,P being a point onE andn anatural number such that theJacobi symbol (−d | n) = −1, if(n + 1)P ≡ 0 (modn).

The number of elliptic pseudoprimes less thanX is bounded above, for largeX, by

${\displaystyle X/\exp ((1/3)\log X\log \log \log X/\log \log X).}$

• 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.

• Weisstein, Eric W."Elliptic Pseudoprime".MathWorld.

This article about anumber is astub. You can help Wikipedia byexpanding it.

• v
• t
• e

• Pseudoprimes
• Number stubs

• Articles with short description
• Short description matches Wikidata
• All stub articles