Found with PFGW Version 3.6.0

509^4604-4604^509 is 2-PRP! (6.0075s+0.0016s)
509^4604-4604^509 is 3-PRP! (5.8666s+0.0034s)
509^4604-4604^509 is 5-PRP! (5.8779s+0.0019s)
509^4604-4604^509 is 7-PRP! (5.8812s+0.0020s)
509^4604-4604^509 is 11-PRP! (5.9009s+0.0018s)

Primality testing 509^4604-4604^509 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.09% and helper 0.00% (0.29% proof)
509^4604-4604^509 is Fermat and Lucas PRP! (29.0035s+0.0018s)

To be completed...