Found with PFGW Version 3.7.5

10957^12444-12444^10957 is 2-PRP! (89.6626s+0.0062s)
10957^12444-12444^10957 is 3-PRP! (92.9274s+0.0051s)
10957^12444-12444^10957 is 5-PRP! (95.1833s+0.0055s)
10957^12444-12444^10957 is 7-PRP! (94.0598s+0.0044s)
10957^12444-12444^10957 is 11-PRP! (93.3438s+0.0047s)

Primality testing 10957^12444-12444^10957 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
10957^12444-12444^10957 is Fermat and Lucas PRP! (567.8656s+0.0061s)

To be completed...