Found with PFGW Version 3.7.5

300^30247+30247^300 is 2-PRP! (111.8077s+0.0043s)
300^30247+30247^300 is 3-PRP! (111.0443s+0.0034s)
300^30247+30247^300 is 5-PRP! (111.6644s+0.0036s)
300^30247+30247^300 is 7-PRP! (117.9077s+0.0028s)
300^30247+30247^300 is 11-PRP! (111.3349s+0.0035s)

Primality testing 300^30247+30247^300 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.03% proof)
300^30247+30247^300 is Fermat and Lucas PRP! (848.1400s+0.0029s)

To be completed...