Somer–Lucas pseudoprime

In mathematics, in particular number theory, an odd composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence $$U(P,Q)$$ with the discriminant $$D=P^2-4Q,$$ such that $$\gcd(N,D)=1$$ and the rank appearance of N in the sequence U(P, Q) is
 * $$\frac{1}{d}\left(N-\left(\frac{D}{N}\right)\right),$$

where $$\left(\frac{D}{N}\right)$$ is the Jacobi symbol.

Applications
Unlike the standard Lucas pseudoprimes, there is no known efficient primality test using the Lucas d-pseudoprimes. Hence they are not generally used for computation.