Found with PFGW Version 3.8.0

10591^12914-12914^10591 is 2-PRP! (48.2688s+0.0145s)
10591^12914-12914^10591 is 3-PRP! (48.7616s+0.0082s)
10591^12914-12914^10591 is 5-PRP! (48.8398s+0.0067s)
10591^12914-12914^10591 is 7-PRP! (48.3318s+0.0097s)
10591^12914-12914^10591 is 11-PRP! (49.6706s+0.0094s)

Primality testing 10591^12914-12914^10591 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.09% proof)
10591^12914-12914^10591 is Fermat and Lucas PRP! (284.2819s+0.0081s)

To be completed...