Found with PFGW Version 3.7.5

3855^5926-5926^3855 is 2-PRP! (15.3874s+0.0021s)
3855^5926-5926^3855 is 3-PRP! (15.0728s+0.0024s)
3855^5926-5926^3855 is 5-PRP! (16.9531s+0.0020s)
3855^5926-5926^3855 is 7-PRP! (14.9482s+0.0020s)
3855^5926-5926^3855 is 11-PRP! (16.0884s+0.0027s)

Primality testing 3855^5926-5926^3855 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N+1 BLS with factored part 0.07% and helper 0.01% (0.22% proof)
3855^5926-5926^3855 is Fermat and Lucas PRP! (87.9563s+0.0070s)

To be completed...