Found with PFGW Version 3.6.0

4884^6299-6299^4884 is 2-PRP! (25.7945s+0.0032s)
4884^6299-6299^4884 is 3-PRP! (28.1772s+0.0021s)
4884^6299-6299^4884 is 5-PRP! (27.0696s+0.0029s)
4884^6299-6299^4884 is 7-PRP! (26.1887s+0.0027s)
4884^6299-6299^4884 is 11-PRP! (25.7219s+0.0021s)

Primality testing 4884^6299-6299^4884 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)
4884^6299-6299^4884 is Fermat and Lucas PRP! (124.2615s+0.0036s)

To be completed...