Code:

Running N+1 test using discriminant 2, base 1+sqrt(2)
(2^13347311+1)/3 is Lucas PRP! (442900.4907s+0.0204s)

and confirming ATH's result:

Code:

Running N+1 test using discriminant 2, base 1+sqrt(2)
(2^13372531+1)/3 is Lucas PRP! (443577.1559s+0.0284s)

The tests for (L+2)^(n+1)==5 (mod n, L^2+1) will take another 3 to 4 weeks