Found with PFGW Version 3.7.5

3813^9742-9742^3813 is 2-PRP! (23.3532s+0.0015s)
3813^9742-9742^3813 is 3-PRP! (22.8788s+0.0014s)
3813^9742-9742^3813 is 5-PRP! (22.7582s+0.0015s)
3813^9742-9742^3813 is 7-PRP! (22.5144s+0.0014s)
3813^9742-9742^3813 is 11-PRP! (22.5418s+0.0014s)

Primality testing 3813^9742-9742^3813 [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 0.02% and helper 0.00% (0.05% proof)
3813^9742-9742^3813 is Fermat and Lucas PRP! (111.7163s+0.0027s)

To be completed...