Found with PFGW Version 3.7.5

302^35829+35829^302 is 2-PRP! (160.1716s+0.0033s)
302^35829+35829^302 is 3-PRP! (160.7690s+0.0035s)
302^35829+35829^302 is 5-PRP! (161.6338s+0.0036s)
302^35829+35829^302 is 7-PRP! (160.5862s+0.0033s)
302^35829+35829^302 is 11-PRP! (160.5171s+0.0034s)

Primality testing 302^35829+35829^302 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)
302^35829+35829^302 is Fermat and Lucas PRP! (911.5017s+0.0031s)

To be completed...