Found with PFGW Version 3.6.0

27^29159-26 is 2-PRP! (20.0499s+0.0042s)
27^29159-26 is 3-PRP! (20.3469s+0.0038s)
27^29159-26 is 5-PRP! (20.0434s+0.0032s)
27^29159-26 is 7-PRP! (20.1968s+0.0030s)
27^29159-26 is 11-PRP! (20.3408s+0.0029s)

Primality testing 27^29159-26 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 23
Running N+1 test using discriminant 37, base 12+sqrt(37)
Calling N-1 BLS with factored part 0.11% and helper 0.02% (0.36% proof)
27^29159-26 is Fermat and Lucas PRP! (174.4472s+0.0042s)

To be completed...