Found with PFGW Version 3.4.8

37^15344+36 is 2-PRP! (40.5024s+0.0443s)
37^15344+36 is 3-PRP! (37.7042s+0.0024s)
37^15344+36 is 5-PRP! (36.8172s+0.0025s)
37^15344+36 is 7-PRP! (36.3432s+0.0024s)
37^15344+36 is 11-PRP! (33.9660s+0.0024s)

Primality testing 37^15344+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 0.03% and helper 0.03% (0.11% proof)
37^15344+36 is Fermat and Lucas PRP! (240.9426s+0.0060s)

To be completed...