Found with PFGW Version 3.6.0

878^4381-4381^878 is 2-PRP! (6.0217s+0.0034s)
878^4381-4381^878 is 3-PRP! (5.9551s+0.0021s)
878^4381-4381^878 is 5-PRP! (5.9604s+0.0033s)
878^4381-4381^878 is 7-PRP! (5.9623s+0.0025s)
878^4381-4381^878 is 11-PRP! (5.9994s+0.0031s)

Primality testing 878^4381-4381^878 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.10% and helper 0.09% (0.40% proof)
878^4381-4381^878 is Fermat and Lucas PRP! (30.7719s+0.0016s)

To be completed...