Found with PFGW Version 3.7.5

7562^10491-10491^7562 is 2-PRP! (34.4888s+0.0027s)
7562^10491-10491^7562 is 3-PRP! (34.5127s+0.0027s)
7562^10491-10491^7562 is 5-PRP! (34.4923s+0.0026s)
7562^10491-10491^7562 is 7-PRP! (34.5040s+0.0026s)
7562^10491-10491^7562 is 11-PRP! (34.4702s+0.0028s)

Primality testing 7562^10491-10491^7562 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
7562^10491-10491^7562 is Fermat and Lucas PRP! (173.5833s+0.0028s)

To be completed...