Found with PFGW Version 3.7.5

37^47844+36 is 3-PRP! (63.5615s+0.0061s)
37^47844+36 is 5-PRP! (62.9477s+0.0062s)
37^47844+36 is 7-PRP! (60.0133s+0.0048s)
37^47844+36 is 11-PRP! (61.8405s+0.0060s)

Primality testing 37^47844+36 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
37^47844+36 is Fermat and Lucas PRP! (486.6022s+0.0089s)

To be completed...