Found with PFGW Version 3.8.0

677^21702+21702^677 is 2-PRP! (67.5444s+0.0070s)
677^21702+21702^677 is 3-PRP! (67.6236s+0.0069s)
677^21702+21702^677 is 5-PRP! (67.5335s+0.0075s)
677^21702+21702^677 is 7-PRP! (67.5206s+0.0071s)
677^21702+21702^677 is 11-PRP! (67.5466s+0.0075s)

Primality testing 677^21702+21702^677 [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 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
677^21702+21702^677 is Fermat and Lucas PRP! (415.7229s+0.0078s)

To be completed...