Found with PFGW Version 3.7.5

1901^5582-5582^1901 is 2-PRP! (12.0623s+0.0006s)
1901^5582-5582^1901 is 3-PRP! (13.2976s+0.0012s)
1901^5582-5582^1901 is 5-PRP! (13.2978s+0.0006s)
1901^5582-5582^1901 is 7-PRP! (12.9825s+0.0006s)
1901^5582-5582^1901 is 11-PRP! (13.5926s+0.0009s)

Primality testing 1901^5582-5582^1901 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 10+sqrt(11)
Calling N+1 BLS with factored part 0.09% and helper 0.04% (0.31% proof)
1901^5582-5582^1901 is Fermat and Lucas PRP! (60.2381s+0.0105s)

To be completed...