Used Multifactor (a modified version of Multisieve) to sieve.
Then pfgw.
(31145!11-1)/86599 is 3-PRP! (280.934000 seconds)
(31145!11-1)/86599 is 7-PRP! (295.725000 seconds)
(31145!11-1)/86599 is 11-PRP! (142.415000 seconds)
(31145!11-1)/86599 is 17-PRP! (306.260000 seconds)
(31145!11-1)/86599 is 37-PRP! (306.130000 seconds)
Primality testing (31145!11-1)/86599 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Calling N-1 BLS with factored part 0.09% and helper 0.05% (0.32% proof)
(31145!11-1)/86599 is Fermat and Lucas PRP! (655.232000 seconds) (digits:11491)

To be completed...