Found with PFGW Version 3.7.5

10427^10580-10580^10427 is 2-PRP! (37.8635s+0.0054s)
10427^10580-10580^10427 is 3-PRP! (37.7620s+0.0032s)
10427^10580-10580^10427 is 5-PRP! (38.1220s+0.0047s)
10427^10580-10580^10427 is 7-PRP! (38.0044s+0.0029s)
10427^10580-10580^10427 is 11-PRP! (38.1163s+0.0030s)

Primality testing 10427^10580-10580^10427 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
10427^10580-10580^10427 is Fermat and Lucas PRP! (187.1633s+0.0029s)

To be completed...