Found with PFGW Version 3.8.0

10955^13158-13158^10955 is 2-PRP! (55.2049s+0.0100s)
10955^13158-13158^10955 is 3-PRP! (55.0740s+0.0113s)
10955^13158-13158^10955 is 5-PRP! (54.8708s+0.0105s)
10955^13158-13158^10955 is 7-PRP! (55.1061s+0.0103s)
10955^13158-13158^10955 is 11-PRP! (54.9194s+0.0104s)

Primality testing 10955^13158-13158^10955 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
10955^13158-13158^10955 is Fermat and Lucas PRP! (272.2429s+0.0106s)

To be completed...