LLR Version 3.8.5 is available!

[ATH]

Thank you. Here is some more information:

Selfridge specified the following parameters for the generation of the Lucas sequences: P = 1 and Q = (1 - D)/4, where D is the first integer in the sequence {5, -7, 9, -11, 13, -15, ...} for which GCD(D,N)=1 and the Jacobi symbol (D|N) = -1. Note, however, that if N is a perfect square, no such D will exist, and the search for D would continue all the way to ±sqrt(N), at which point GCD(D,N)=sqrt(N) would expose N as composite. Consequently, the algorithm also presumes the presence of a preliminary check for perfect squares (as well as even integers and integers < 3).

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