Found with PFGW Version 3.7.5

4023^10520-10520^4023 is 2-PRP! (26.6017s+0.0016s)
4023^10520-10520^4023 is 3-PRP! (26.0691s+0.0016s)
4023^10520-10520^4023 is 5-PRP! (26.5826s+0.0015s)
4023^10520-10520^4023 is 7-PRP! (26.2630s+0.0017s)
4023^10520-10520^4023 is 11-PRP! (26.0669s+0.0015s)

Primality testing 4023^10520-10520^4023 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
4023^10520-10520^4023 is Fermat and Lucas PRP! (202.7664s+0.0082s)

To be completed...