Found with PFGW Version 3.7.5

23^35328+22 is 2-PRP! (33.4127s+0.0066s)
23^35328+22 is 3-PRP! (34.2007s+0.0078s)
23^35328+22 is 5-PRP! (34.1597s+0.0088s)
23^35328+22 is 7-PRP! (33.1988s+0.0079s)
23^35328+22 is 11-PRP! (34.2348s+0.0062s)

Primality testing 23^35328+22 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.19% proof)
23^35328+22 is Fermat and Lucas PRP! (264.0315s+0.0084s)

To be completed...