Found with PFGW Version 3.8.0

5552^12691-12691^5552 is 2-PRP! (42.6758s+0.0043s)
5552^12691-12691^5552 is 3-PRP! (42.2341s+0.0047s)
5552^12691-12691^5552 is 5-PRP! (42.1544s+0.0051s)
5552^12691-12691^5552 is 7-PRP! (42.2847s+0.0054s)
5552^12691-12691^5552 is 11-PRP! (42.1522s+0.0050s)

Primality testing 5552^12691-12691^5552 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
5552^12691-12691^5552 is Fermat and Lucas PRP! (257.1015s+0.0093s)

To be completed...