Well, here comes 6-th largest PRP @ 502485 digits ;-)

(2^1669219-2^834610+1)/5 is 5-PRP, originally found using LLR ver.3.8.4 for Windows (no factor till 2^54).

This is a Fermat PRP at base 3, 5, 7, 11, 13, 31, 101, 137 - confirmed with PFGW ver.3.4.4 for Windows (32-bit).

Additionally using the following command with PFGW:

pfgw -l -tc -q(2^1669219-2^834610+1)/5

I've received the following result:

Code:

Primality testing (2^1669219-2^834610+1)/5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 11
Running N-1 test using base 19
Running N-1 test using base 29
Running N+1 test using discriminant 37, base 2+sqrt(37)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
(2^1669219-2^834610+1)/5 is Fermat and Lucas PRP! (229144.7431s+0.0642s)