Found with PFGW Version 3.6.0

4625^4712-4712^4625 is 2-PRP! (13.4651s+0.0024s)
4625^4712-4712^4625 is 3-PRP! (13.4074s+0.0022s)
4625^4712-4712^4625 is 5-PRP! (13.2534s+0.0021s)
4625^4712-4712^4625 is 7-PRP! (13.3385s+0.0022s)
4625^4712-4712^4625 is 11-PRP! (13.5580s+0.0026s)

Primality testing 4625^4712-4712^4625 [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 0.03% and helper 0.01% (0.09% proof)
4625^4712-4712^4625 is Fermat and Lucas PRP! (64.8135s+0.0023s)

To be completed...