sorry but whaaaaaaaat?
 

[code]
10736638*537^2-1 is base 3-Strong Fermat PRP! Time : 3.456 ms.
10736638*537^2-1 is Frobenius PRP! (P = 4, Q = 2, D = 8) Time : 7.734 ms.
10736638 > 537^2, so, only a Strong PRP test is done for 10736638*537^2+1.
10736638*537^2+1 is base 3-Strong Fermat PRP! Time : 3.349 ms.
10736638*537^2+1 is Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 7.178 ms.
10736638*537^2+5 is base 3-Strong Fermat PRP! Time : 3.508 ms.
10736638*537^2+5 is Frobenius PRP! (P = 4, Q = 2, D = 8) Time : 7.632 ms.
10736638*537^2+7 is base 3-Strong Fermat PRP! Time : 3.244 ms.
10736638*537^2+7 is Frobenius PRP! (P = 4, Q = 2, D = 8) Time : 7.258 ms.
[/code]did I make a mistake somewhere or all those are considered as pseudoprime? (or even prime)

Which version of LLR you're using?

3.8.0

These 4 numbers are all prime! (Quick test with Alptertron's ECM-applet).

Because k >> n, LLR can only do those tests.

if anyone is interested, I have a small list availlable