Found with PFGW Version 3.8.0

10010^10951-10951^10010 is 2-PRP! (35.9405s+0.0039s)
10010^10951-10951^10010 is 3-PRP! (35.9298s+0.0045s)
10010^10951-10951^10010 is 5-PRP! (35.8639s+0.0051s)
10010^10951-10951^10010 is 7-PRP! (37.6641s+0.0045s)
10010^10951-10951^10010 is 11-PRP! (35.7961s+0.0045s)

Primality testing 10010^10951-10951^10010 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
10010^10951-10951^10010 is Fermat and Lucas PRP! (183.4901s+0.0070s)

To be completed...