Found with PFGW Version 3.8.0

348^17635-17635^348 is 2-PRP! (37.0080s+0.0042s)
348^17635-17635^348 is 3-PRP! (39.3503s+0.0054s)
348^17635-17635^348 is 5-PRP! (38.3171s+0.0044s)
348^17635-17635^348 is 7-PRP! (38.1352s+0.0048s)
348^17635-17635^348 is 11-PRP! (37.9868s+0.0048s)

Primality testing 348^17635-17635^348 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
348^17635-17635^348 is Fermat and Lucas PRP! (193.6134s+0.0084s)

To be completed...