Found with PFGW Version 3.4.6

26^14058+25 is 2-PRP! (12.8663s+0.0045s)
26^14058+25 is 3-PRP! (13.3680s+0.0043s)
26^14058+25 is 5-PRP! (17.5649s+0.0170s)
26^14058+25 is 7-PRP! (17.2207s+0.0044s)
26^14058+25 is 11-PRP! (16.7785s+0.0110s)

Primality testing 26^14058+25 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 31
Running N+1 test using discriminant 41, base 10+sqrt(41)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
26^14058+25 is Fermat and Lucas PRP! (204.7052s+0.0200s)

To be completed...