Found with PFGW Version 3.7.5

5918^10739-10739^5918 is 2-PRP! (35.3121s+0.0016s)
5918^10739-10739^5918 is 3-PRP! (35.1526s+0.0016s)
5918^10739-10739^5918 is 5-PRP! (35.0037s+0.0017s)
5918^10739-10739^5918 is 7-PRP! (34.7822s+0.0017s)
5918^10739-10739^5918 is 11-PRP! (34.8259s+0.0018s)

Primality testing 5918^10739-10739^5918 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.07% proof)
5918^10739-10739^5918 is Fermat and Lucas PRP! (203.9283s+0.0033s)

To be completed...