PFGW:
Primality testing (37*10^55359+53)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.14% proof)
(37*10^55359+53)/9 is Fermat and Lucas PRP! (907.1833s+0.0028s)

Primality testing (37*10^86230+53)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
(37*10^86230+53)/9 is Fermat and Lucas PRP! (2142.9121s+0.0048s)

To be completed...