Used Multifactor (a modified version of Multisieve) to sieve.
Then pfgw.
(31790!11-1)/5309 is 3-PRP! (167.401000 seconds)
(31790!11-1)/5309 is 7-PRP! (294.964000 seconds)
(31790!11-1)/5309 is 11-PRP! (288.485000 seconds)
(31790!11-1)/5309 is 17-PRP! (286.121000 seconds)
(31790!11-1)/5309 is 37-PRP! (286.632000 seconds)
Primality testing (31790!11-1)/5309 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Calling N-1 BLS with factored part 0.07% and helper 0.03% (0.24% proof)
(31790!11-1)/5309 is Fermat and Lucas PRP! (1633.609000 seconds) (digits:11755)

To be completed...