Found with PFGW Version 3.6.0

4267^6560-6560^4267 is 2-PRP! (23.1902s+0.0022s)
4267^6560-6560^4267 is 3-PRP! (23.2226s+0.0020s)
4267^6560-6560^4267 is 5-PRP! (23.2525s+0.0021s)
4267^6560-6560^4267 is 7-PRP! (23.2301s+0.0023s)
4267^6560-6560^4267 is 11-PRP! (23.2126s+0.0022s)

Primality testing 4267^6560-6560^4267 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.22% proof)
4267^6560-6560^4267 is Fermat and Lucas PRP! (110.5120s+0.0035s)

To be completed...