Found with PFGW Version 3.6.0

1248^3667-3667^1248 is 2-PRP! (5.6752s+0.0034s)
1248^3667-3667^1248 is 3-PRP! (5.6990s+0.0017s)
1248^3667-3667^1248 is 5-PRP! (5.7615s+0.0017s)
1248^3667-3667^1248 is 7-PRP! (5.9339s+0.0085s)
1248^3667-3667^1248 is 11-PRP! (5.7185s+0.0031s)

Primality testing 1248^3667-3667^1248 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N-1 BLS with factored part 0.13% and helper 0.08% (0.46% proof)
1248^3667-3667^1248 is Fermat and Lucas PRP! (31.2345s+0.0037s)

To be completed...