Found with PFGW Version 3.7.5

4094^7829-7829^4094 is 2-PRP! (40.0759s+0.0028s)
4094^7829-7829^4094 is 3-PRP! (39.4167s+0.0029s)
4094^7829-7829^4094 is 5-PRP! (39.9024s+0.0027s)
4094^7829-7829^4094 is 7-PRP! (27.0690s+0.0026s)
4094^7829-7829^4094 is 11-PRP! (31.2917s+0.0023s)

Primality testing 4094^7829-7829^4094 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.05% proof)
4094^7829-7829^4094 is Fermat and Lucas PRP! (240.4502s+0.0067s)

To be completed...