Found with PFGW Version 3.7.5

4577^10520-10520^4577 is 2-PRP! (27.0430s+0.0016s)
4577^10520-10520^4577 is 3-PRP! (26.5085s+0.0016s)
4577^10520-10520^4577 is 5-PRP! (27.0148s+0.0015s)
4577^10520-10520^4577 is 7-PRP! (26.4558s+0.0017s)
4577^10520-10520^4577 is 11-PRP! (26.5071s+0.0015s)

Primality testing 4577^10520-10520^4577 [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 0.04% and helper 0.02% (0.14% proof)
4577^10520-10520^4577 is Fermat and Lucas PRP! (162.2423s+0.0027s)

To be completed...