Found with PFGW Version 3.4.6

26^10876+25 is 2-PRP! (6.0498s+0.0046s)
26^10876+25 is 3-PRP! (6.1928s+0.0013s)
26^10876+25 is 5-PRP! (6.1117s+0.0011s)
26^10876+25 is 7-PRP! (7.4095s+0.0013s)
26^10876+25 is 11-PRP! (7.7894s+0.0011s)

Primality testing 26^10876+25 [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 0.27% and helper 0.07% (0.89% proof)
26^10876+25 is Fermat and Lucas PRP! (44.5501s+0.0040s)

To be completed...