Found with PFGW Version 3.7.5

267^26336+26336^267 is 2-PRP! (176.5204s+0.0051s)
267^26336+26336^267 is 3-PRP! (176.7273s+0.0048s)
267^26336+26336^267 is 5-PRP! (178.7106s+0.0054s)
267^26336+26336^267 is 7-PRP! (175.5940s+0.0047s)
267^26336+26336^267 is 11-PRP! (180.5763s+0.0054s)

Primality testing 267^26336+26336^267 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
267^26336+26336^267 is Fermat and Lucas PRP! (976.3426s+0.0053s)

To be completed...