Found with PFGW Version 3.7.5

4630^5829-5829^4630 is 2-PRP! (15.4486s+0.0024s)
4630^5829-5829^4630 is 3-PRP! (15.4315s+0.0021s)
4630^5829-5829^4630 is 5-PRP! (15.5605s+0.0026s)
4630^5829-5829^4630 is 7-PRP! (15.2723s+0.0019s)
4630^5829-5829^4630 is 11-PRP! (15.3434s+0.0025s)

Primality testing 4630^5829-5829^4630 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.07% and helper 0.03% (0.24% proof)
4630^5829-5829^4630 is Fermat and Lucas PRP! (92.2329s+0.0042s)

To be completed...