The teacher told each of the $$3$$ students A, B and C a different prime number, and each of them knew only his or her own number. The teacher said, "Your numbers are different from each other, and none of them is more than $$45$$." Later, they have the conversation below:  A: "Our $$3$$ numbers cannot form a correct addition equation of $$\square + \square = \square $$."  B: "I don\textquotesingle t know how many you are, but I know that if I subtract $$1$$ from my number, our difference is $7$."  C: "If you multiply me by $$2$$, can we form a correct addition equation?"  Teacher: "Yes, if you multiply C\textquotesingle s number by $$2$$, your three numbers will be able to form an addition equation."  If all three students are smart and honest enough, then the sum of these $$3$$ prime numbers is~\uline{~~~~~~~~~~}~. 
Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers