Found with PFGW Version 3.8.0

10751^13298-13298^10751 is 2-PRP! (61.8775s+0.0074s)
10751^13298-13298^10751 is 3-PRP! (61.6470s+0.0067s)
10751^13298-13298^10751 is 5-PRP! (61.8696s+0.0141s)
10751^13298-13298^10751 is 7-PRP! (61.7344s+0.0066s)
10751^13298-13298^10751 is 11-PRP! (61.8128s+0.0104s)

Primality testing 10751^13298-13298^10751 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
10751^13298-13298^10751 is Fermat and Lucas PRP! (301.8397s+0.0069s)

To be completed...