Found with PFGW Version 3.6.0

37^25293+36 is 2-PRP! (24.1618s+0.0044s)
37^25293+36 is 3-PRP! (23.8936s+0.0042s)
37^25293+36 is 5-PRP! (24.0417s+0.0028s)
37^25293+36 is 7-PRP! (23.9967s+0.0030s)
37^25293+36 is 11-PRP! (24.1552s+0.0029s)

Primality testing 37^25293+36 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 6+sqrt(23)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
37^25293+36 is Fermat and Lucas PRP! (192.3131s+0.0052s)

To be completed...