Found with PFGW Version 3.7.5

691^8834-8834^691 is 2-PRP! (10.4018s+0.0012s)
691^8834-8834^691 is 3-PRP! (10.4573s+0.0010s)
691^8834-8834^691 is 5-PRP! (10.3556s+0.0011s)
691^8834-8834^691 is 7-PRP! (10.4168s+0.0011s)
691^8834-8834^691 is 11-PRP! (10.3805s+0.0012s)

Primality testing 691^8834-8834^691 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
691^8834-8834^691 is Fermat and Lucas PRP! (52.6252s+0.0021s)

To be completed...