18. Four different prime numbers $a, b, c, d$ satisfy the following properties:
(1) $a+b+c+d$ is also a prime number;
(2) The sum of two of $a, b, c, d$ is also a prime number:
(3) The sum of three of $a, b, c, d$ is also a prime number. The smallest value of $a+b+c+d$ that satisfies the conditions is $\qquad$
【Analysis】Given that $a+b+c+d$ is a prime number, we know that 2 must be one of them. Let's assume $a=2$. Since the sum of any three numbers is also a prime number, it can only be $\mathrm{b}+\mathrm{c}+\mathrm{d}$ that is a prime number. We can start with the smallest possible values, and we find that the solutions are $2,3,7,19$ or 2, 5, 7, 17. Therefore, the minimum value of $a+b+c+d$ is 31.