(2^125929+2^62965+1)/5 is base 11-PRP! Time: 47.697 sec.
(2^221891-2^110946+1)/5 is base 5-PRP! Time: 172.246 sec.
(2^235099-2^117550+1)/5 is base 5-PRP! Time: 182.456 sec.
(2^305867-2^152934+1)/5 is base 5-PRP! Time: 318.612 sec.
(2^311027-2^155514+1)/5 is base 5-PRP! Time: 335.017 sec.
(2^333227-2^166614+1)/5 is base 5-PRP! Time: 677.060 sec.
(2^365689+2^182845+1)/5 is base 11-PRP! Time: 1346.151 sec.

All these numbers are quotient by 5 of the Aurifeuillan cofactor of a
4^p+1 number, p being prime. The other Aurifeuillan factor is a Gaussian-Mersenne norm. They have been prefactored up to 40 bits factors. The base used in each test is the same that the one used to do the Proth primality test of the Gaussian-Mersenne norm factor.
All the PRP tests shown here are strong Fermat.
I also did recently Lucas N+1 PRP tests on all these numbers.

To be completed...