Found with PFGW Version 3.6.0

4670^4889-4889^4670 is 2-PRP! (13.6733s+0.0026s)
4670^4889-4889^4670 is 3-PRP! (13.6311s+0.0024s)
4670^4889-4889^4670 is 5-PRP! (13.5222s+0.0023s)
4670^4889-4889^4670 is 7-PRP! (13.6795s+0.0023s)
4670^4889-4889^4670 is 11-PRP! (13.5314s+0.0022s)

Primality testing 4670^4889-4889^4670 [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 0.06% and helper 0.01% (0.18% proof)
4670^4889-4889^4670 is Fermat and Lucas PRP! (65.7135s+0.0040s)

To be completed...