Found with PFGW Version 3.7.5

3900^12643+12643^3900 is 2-PRP! (40.1970s+0.0023s)
3900^12643+12643^3900 is 3-PRP! (40.4681s+0.0023s)
3900^12643+12643^3900 is 5-PRP! (39.8396s+0.0023s)
3900^12643+12643^3900 is 7-PRP! (39.8462s+0.0023s)
3900^12643+12643^3900 is 11-PRP! (41.0881s+0.0024s)

Primality testing 3900^12643+12643^3900 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.03% and helper 0.03% (0.12% proof)
3900^12643+12643^3900 is Fermat and Lucas PRP! (240.8605s+0.0026s)

To be completed...