Found with PFGW Version 3.4.8

45^11536+44 is 2-PRP! (12.9980s+0.0050s)
45^11536+44 is 3-PRP! (14.0418s+0.0165s)
45^11536+44 is 5-PRP! (18.3200s+0.0052s)
45^11536+44 is 7-PRP! (23.4579s+0.0064s)
45^11536+44 is 11-PRP! (26.8520s+0.0064s)

Primality testing 45^11536+44 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 2+sqrt(7)
Calling N+1 BLS with factored part 0.08% and helper 0.06% (0.30% proof)
45^11536+44 is Fermat and Lucas PRP! (206.8762s+0.0168s)

To be completed...