Prime95: PRP-3
PFGW: Fermat and Lucas PRP

If n mod 74256 == 66006, then 10^n+7 is divisible by 337 and by 443.
363030 = 66006 + 4*74256.
n = 363030 is the smallest n, such that (10^n+7)/337/443 is prime.

To be completed...