Found with PFGW Version 3.4.6

37^7969+36 is 2-PRP! (4.8116s+0.0043s)
37^7969+36 is 3-PRP! (5.5098s+0.0045s)
37^7969+36 is 5-PRP! (5.0429s+0.0050s)
37^7969+36 is 7-PRP! (4.9585s+0.0047s)
37^7969+36 is 11-PRP! (4.9104s+0.0045s)

Primality testing 37^7969+36 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N+1 BLS with factored part 0.21% and helper 0.01% (0.64% proof)
37^7969+36 is Fermat and Lucas PRP! (35.4979s+0.0089s)

To be completed...