35 consecutive positive integers can be set as n- 17, n- 16, ..., n+ 16, n+ 17, where the integer n >；; 17

It is easy to see that their sum is 35n.

From abcd = 35n, and A, B, C and D are prime numbers, we can know that one of A, B, C and D is 5 and the other is 7.

Let a = 5 and b = 7, so n = cd is the product of two prime numbers.

Minimize a+b+c+d, that is, minimize c+d.

Consider an integer greater than 17, which can be expressed as the product of two prime numbers, namely 2 1, 22, 25, 26, ...

Corresponding to C+D = 10, 13, 10, 15, ...

When n > 25, by (c+d)? = (c-d)？ +4cd≥4cd = 4n & gt； 100 indicates that c+d > 10.

So the minimum value of c+d is 10.

The minimum value of a+b+c+d is 22, which is obtained when (a, b, c, d) = (3, 5, 7, 7) or (5, 5, 5, 7) and its substitution.

Add operation

In the formula with brackets, the inside of brackets should be counted first, then the inside of brackets, and finally the outside of brackets.

1, elementary arithmetic order: when operating at the same level, it is calculated from left to right in turn; Two-stage operation, first multiply and then divide, then add and subtract.

When there are brackets, count the inside of brackets first, and then count the outside of brackets; When there are multiple brackets, count the brackets first, then the brackets inside, then the braces inside, and finally the brackets outside.

2. Multiplication is a simple operation of addition and division is a simple operation of subtraction. Subtraction and addition are reciprocal operations, and division and multiplication are reciprocal operations.

When several addends are added, the positions of addends can be exchanged at will; Or add a few addends first and then add them with other addends, and the sum remains the same.

Subtracting the sum of two numbers from a number is equivalent to subtracting each addend in the sum from this number in turn.