Found with PFGW Version 3.7.5

739^5624-5624^739 is 2-PRP! (8.4617s+0.0015s)
739^5624-5624^739 is 3-PRP! (9.6334s+0.0014s)
739^5624-5624^739 is 5-PRP! (9.4599s+0.0018s)
739^5624-5624^739 is 7-PRP! (9.3260s+0.0020s)
739^5624-5624^739 is 11-PRP! (9.7380s+0.0015s)

Primality testing 739^5624-5624^739 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.15% proof)
739^5624-5624^739 is Fermat and Lucas PRP! (45.5165s+0.0036s)

To be completed...