Found with PFGW Version 3.4.8

2378^3135-3135^2378 is 2-PRP! (20.1181s+0.0087s)
2378^3135-3135^2378 is 3-PRP! (26.1099s+0.0061s)
2378^3135-3135^2378 is 5-PRP! (26.9776s+0.0064s)
2378^3135-3135^2378 is 7-PRP! (27.5021s+0.0056s)
2378^3135-3135^2378 is 11-PRP! (27.4529s+0.0074s)

Primality testing 2378^3135-3135^2378 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.08% and helper 0.07% (0.31% proof)
2378^3135-3135^2378 is Fermat and Lucas PRP! (119.3029s+0.0145s)

To be completed...