Found with PFGW Version 3.7.5

4639^7284-7284^4639 is 2-PRP! (49.9954s+0.0033s)
4639^7284-7284^4639 is 3-PRP! (48.0389s+0.0015s)
4639^7284-7284^4639 is 5-PRP! (45.7923s+0.0018s)
4639^7284-7284^4639 is 7-PRP! (47.3820s+0.0017s)
4639^7284-7284^4639 is 11-PRP! (48.4159s+0.0034s)

Primality testing 4639^7284-7284^4639 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
4639^7284-7284^4639 is Fermat and Lucas PRP! (244.2574s+0.0045s)

To be completed...