Found with PFGW Version 3.7.5

243^37738+37738^243 is 2-PRP! (169.4106s+0.0033s)
243^37738+37738^243 is 3-PRP! (163.8678s+0.0032s)
243^37738+37738^243 is 5-PRP! (163.8780s+0.0028s)
243^37738+37738^243 is 7-PRP! (164.3633s+0.0032s)
243^37738+37738^243 is 11-PRP! (164.3959s+0.0030s)

Primality testing 243^37738+37738^243 [N-1/N+1, Brillhart-Lehmer-Selfridge]
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 0.02% and helper 0.00% (0.05% proof)
243^37738+37738^243 is Fermat and Lucas PRP! (975.5842s+0.0032s)

To be completed...