Found with PFGW Version 3.6.0

4386^4643-4643^4386 is 2-PRP! (12.7756s+0.0038s)
4386^4643-4643^4386 is 3-PRP! (12.9151s+0.0024s)
4386^4643-4643^4386 is 5-PRP! (13.1002s+0.0024s)
4386^4643-4643^4386 is 7-PRP! (14.6598s+0.0023s)
4386^4643-4643^4386 is 11-PRP! (15.8051s+0.0023s)

Primality testing 4386^4643-4643^4386 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.11% and helper 0.06% (0.38% proof)
4386^4643-4643^4386 is Fermat and Lucas PRP! (61.4313s+0.0041s)

To be completed...