Found with PFGW Version 3.8.0

4448^11243-11243^4448 is 2-PRP! (33.9543s+0.0061s)
4448^11243-11243^4448 is 3-PRP! (35.9630s+0.0060s)
4448^11243-11243^4448 is 5-PRP! (37.4884s+0.0063s)
4448^11243-11243^4448 is 7-PRP! (34.7677s+0.0063s)
4448^11243-11243^4448 is 11-PRP! (34.8368s+0.0066s)

Primality testing 4448^11243-11243^4448 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
4448^11243-11243^4448 is Fermat and Lucas PRP! (169.8723s+0.0072s)

To be completed...