The starting value u0 will be the Lucas sequence term Vk(P,1) taken modulo N. This process of selection takes very little time compared to the main test.
If a satisfies a quadratic equation, then this is a Lucas sequence, and has an expression of the form v(i) = α v(i−1) + β v(i−2).
[4] The software is used by both individual prime searchers and some distributed computing projects including Riesel Sieve and PrimeGrid.
[6] This generates a "proof of work" certificate which allows the computation to be verified without needing a full double-check.
A further update, PRST[7] uses an alternate certificate scheme[8] which takes longer to verify but is faster to generate for some forms of prime.