Found with PFGW Version 3.8.0

7^116240-116240^7 is 2-PRP! (182.8407s+0.0094s)
7^116240-116240^7 is 3-PRP! (187.0196s+0.0108s)
7^116240-116240^7 is 5-PRP! (178.6122s+0.0075s)
7^116240-116240^7 is 7-PRP! (184.5071s+0.0142s)
7^116240-116240^7 is 11-PRP! (179.4397s+0.0066s)

Primality testing 7^116240-116240^7 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.06% proof)
7^116240-116240^7 is Fermat and Lucas PRP! (893.3844s+0.0105s)

To be completed...