Found with PFGW Version 3.7.5

4691^10818-10818^4691 is 2-PRP! (34.1111s+0.0011s)
4691^10818-10818^4691 is 3-PRP! (34.4074s+0.0011s)
4691^10818-10818^4691 is 5-PRP! (33.8719s+0.0015s)
4691^10818-10818^4691 is 7-PRP! (33.7964s+0.0012s)
4691^10818-10818^4691 is 11-PRP! (33.8585s+0.0010s)

Primality testing 4691^10818-10818^4691 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
4691^10818-10818^4691 is Fermat and Lucas PRP! (203.7436s+0.0018s)

To be completed...