Found with PFGW Version 3.7.5

4705^5924-5924^4705 is 2-PRP! (15.9462s+0.0021s)
4705^5924-5924^4705 is 3-PRP! (15.6128s+0.0027s)
4705^5924-5924^4705 is 5-PRP! (17.6853s+0.0020s)
4705^5924-5924^4705 is 7-PRP! (15.1298s+0.0043s)
4705^5924-5924^4705 is 11-PRP! (17.3641s+0.0019s)

Primality testing 4705^5924-5924^4705 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.08% and helper 0.02% (0.27% proof)
4705^5924-5924^4705 is Fermat and Lucas PRP! (93.5376s+0.0056s)

To be completed...