Found with PFGW Version 3.8.0

4483^13088-13088^4483 is 2-PRP! (46.7017s+0.0080s)
4483^13088-13088^4483 is 3-PRP! (43.6937s+0.0081s)
4483^13088-13088^4483 is 5-PRP! (44.4228s+0.0086s)
4483^13088-13088^4483 is 7-PRP! (42.6848s+0.0142s)
4483^13088-13088^4483 is 11-PRP! (43.1360s+0.0082s)

Primality testing 4483^13088-13088^4483 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 9+sqrt(23)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.06% proof)
4483^13088-13088^4483 is Fermat and Lucas PRP! (259.9884s+0.0092s)

To be completed...