Found with PFGW Version 3.7.5

2183^5378-5378^2183 is 2-PRP! (11.0053s+0.0033s)
2183^5378-5378^2183 is 3-PRP! (10.3384s+0.0036s)
2183^5378-5378^2183 is 5-PRP! (12.0471s+0.0027s)
2183^5378-5378^2183 is 7-PRP! (10.3435s+0.0020s)
2183^5378-5378^2183 is 11-PRP! (10.4766s+0.0020s)

Primality testing 2183^5378-5378^2183 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
2183^5378-5378^2183 is Fermat and Lucas PRP! (57.5950s+0.0033s)

To be completed...