Found with PFGW Version 3.8.0

713^27118+27118^713 is 2-PRP! (110.4179s+0.0052s)
713^27118+27118^713 is 3-PRP! (109.0215s+0.0082s)
713^27118+27118^713 is 5-PRP! (114.5281s+0.0083s)
713^27118+27118^713 is 7-PRP! (108.9006s+0.0083s)
713^27118+27118^713 is 11-PRP! (110.2794s+0.0083s)

Primality testing 713^27118+27118^713 [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 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.03% proof)
713^27118+27118^713 is Fermat and Lucas PRP! (739.8263s+0.0091s)

To be completed...