Assuming I have the rest correct, given 17dn, 11dn and 14dn, then 16ac looks like xAByC where A, B and C are known and the digits add up to 1ac - 4.
Thus 16ac is one of 1AB3C, 2AB2C, 3AB1C or 4AB0C. But only one of those is prime; hence the constraint about the number of factors of 13dn is not needed.
Is that all correct, or have I made an error somewhere?