Found with PFGW Version 3.6.0

4984^12471-12471^4984 is 2-PRP! (97.7984s+0.0037s)
4984^12471-12471^4984 is 3-PRP! (96.4610s+0.0036s)
4984^12471-12471^4984 is 5-PRP! (98.9780s+0.0025s)
4984^12471-12471^4984 is 7-PRP! (97.5390s+0.0048s)
4984^12471-12471^4984 is 11-PRP! (98.2402s+0.0023s)

Primality testing 4984^12471-12471^4984 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.07% proof)
4984^12471-12471^4984 is Fermat and Lucas PRP! (460.1348s+0.0052s)

To be completed...