Strong Elliptic Pseudoprime

Let $n$ be an Elliptic Pseudoprime associated with $(E,P)$, and let $n+1=2^s k$ with $k$ Odd and $s\geq 0$. Then $n$ is a strong elliptic pseudoprime when either $kP\equiv 0\ \left({{\rm mod\ } {n}}\right)$ or $2^rkP\equiv 0\ \left({{\rm mod\ } {n}}\right)$ for some $r$ with $1\leq r<s$.

See also Elliptic Pseudoprime

References

Ribenboim, P. The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 132-134, 1996.