pg(308899)
 

pg(69660) is prime
pg(92020) is prime and 92020+239239 is prime
pg(92020+239239) is prime




Now i consider


pg(69660+239239) which is (2^308899-1)*10^92988+2^308898-1




the number is not prime ( I think I already tested it with Pfgw) but has no small factors.