Found with PFGW Version 3.6.0

6753^10024-10024^6753 is 2-PRP! (68.7288s+0.0036s)
6753^10024-10024^6753 is 3-PRP! (68.3477s+0.0061s)
6753^10024-10024^6753 is 5-PRP! (69.3127s+0.0035s)
6753^10024-10024^6753 is 7-PRP! (68.5141s+0.0035s)
6753^10024-10024^6753 is 11-PRP! (71.4977s+0.0035s)

Primality testing 6753^10024-10024^6753 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.03% (0.12% proof)
6753^10024-10024^6753 is Fermat and Lucas PRP! (375.3236s+0.0051s)

To be completed...