Editted pfgw output:
10^10001+16737 is Fermat and Lucas PRP!
10^10001+92551 is Fermat and Lucas PRP!
10^10001+159661 is Fermat and Lucas PRP!
10^10001+217081 is Fermat and Lucas PRP!
10^10001+232417 is Fermat and Lucas PRP!
10^10001+237523 is Fermat and Lucas PRP!
10^10001+253207 is Fermat and Lucas PRP!
10^10001+255967 is Fermat and Lucas PRP!
10^10001+285457 is Fermat and Lucas PRP!
10^10001+383569 is Fermat and Lucas PRP!
10^10001+404787 is Fermat and Lucas PRP!
10^10001+413913 is Fermat and Lucas PRP!
10^10001+436513 is Fermat and Lucas PRP!
10^10001+500923 is Fermat and Lucas PRP!

To be completed...