@Jean --
Ah, before I forgot.
This may need to be implemented (I usually now run it externally with Pari/GP); you may already have a [C]legendre()[/C] or [C]kronecker()[/C] implementation in LLR code.

This has to do with choice of 'a' value. Anand 'axn' Nair suggested a minimal quick check.
This is pseudo-code:
[CODE]while (kronecker(a,N) >= 0) { // then do not use this 'a'
// chose next 'a'
}[/CODE]
This is why I skipped values 3, 5 for the latest long-running test, and skipped immediately to 7, 11, 13 (I provided them in llr.ini).
Because there were only two p*q factors in the base b (semiprime), all three of these worked in a single pass each. This is not going to be always the case. Restarts will still be needed, especially when base has many factors (see unit test with 93500 = 2^2*5^3*11*17 )