Found with PFGW Version 3.8.0

7337^12542-12542^7337 is 2-PRP! (43.2779s+0.0044s)
7337^12542-12542^7337 is 3-PRP! (43.0523s+0.0093s)
7337^12542-12542^7337 is 5-PRP! (43.2343s+0.0073s)
7337^12542-12542^7337 is 7-PRP! (44.2487s+0.0075s)
7337^12542-12542^7337 is 11-PRP! (43.1176s+0.0078s)

Primality testing 7337^12542-12542^7337 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
7337^12542-12542^7337 is Fermat and Lucas PRP! (248.9302s+0.0086s)

To be completed...