How many different ways are there to split 37 into the sum of several different prime numbers? 5

Prime numbers below 37 are 3 5 7 11 13 17 19 23 29 31

31+3+3 once.

29+5+3 once.

23+11+3 23+7+7 twice.

19+13+5 19+11+7 19+7+5+3+3 19+5+5+5+5+3,19+3+3+3+3+3+3 5 times.

17+17+3 17+13+7 17+11+3+3+3 17+7+5+5+3 17+7+7+3+3 17+5+5+5+5 17+3+3+3+3+3+3+5 7 types.

13+13+11 13+11+7+3+3 13+11+5+5+3 13+7+7+7+3 13+7+7+5+5 13+7+5+3+3+3+3,13+5+5+5+3+3+3+3,13+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+

11+11+7+5+3,11+11+5+5+5,11+11+3+3+3+3+3,11+7+7+7+7+5,11+7+7+3+3+3+3,11+7+5+5+3+3+3,11+5+5+5+5+5+3+3,11+5+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+

7+7+7+7+3+3+3,7+7+7+5+5+3+3,7+7+5+5+5+5+3+3,7+5+5+5+5+5+5+5,7+5+5+5+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+

5+5+5+5+5+5+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3 II.

There are 40 such algorithms.

If repeated summaries are not allowed, there are only 5 kinds.

There is no punctuation in the question year, there is ambiguity! It is also difficult to understand what is meant by "the product of the poor prime numbers". Do you want to ask this question: divide 27 into the sum of three prime numbers, so that the product of these three prime numbers is maximized? What are these three prime numbers?

Among the above seven splitting methods, the last four types do not meet the requirements of "different prime numbers". In the third of the first three splitting methods, the product of the three prime numbers is the largest, so the three prime numbers are and 13.

Do you need to ask? 3 for sure.

To decompose 33 into an even number of prime numbers, there must be 2. Also, for the same even number, decompose into two numbers that differ less, and the product of the two numbers is greater. Because, these two numbers can be set as a+b and a-b, where a+b is a fixed value, (a+b)*(a-b)=a2-b2, obviously the smaller b, the larger a, the larger the product.

When divided into two prime numbers. It can only be 2+31, 2*31=62;

When divided into three prime numbers. When the decomposed prime number contains 3, the product is the largest when decomposed into 3+13+17, 3*13*17=663;

When the decomposed prime number contains 5 and does not contain 3, the product is the largest when decomposed to 5+11+17, and 5*11*17=935;A factored prime number cannot be factored if it contains 7 and does not contain 3 and 5. When a factored prime number contains 11 or greater numbers and does not contain 3, 5, 7, because 33 is three times that of 11, it obviously cannot be factored.

When divided into four prime numbers. One of them is 2. When the decomposed prime number contains 3, it is the largest when decomposed to 2+3+11+17, and 2*3*11*17=1122;When the decomposed prime number contains 5 and does not contain 3, the decomposition is 2+5+7+19 at the maximum, and 2*5*7*19=1330;When the decomposed prime number contains 7 and does not include 3 and 5, the decomposition is 2+7+11+13 at the maximum, and 2*7*11*13=2002. In the same way, if the decomposed prime number contains 11 or greater numbers, and does not contain 3, 5, and 7, it cannot be decomposed.

When decomposed into five prime numbers, the sum of the smallest five prime numbers is 3+5+7+11+13=39>33 and cannot be decomposed.

Therefore, when 33 is decomposed into 2, 7, 11, 13, the product of the prime number is the largest.

31=3*9+2*2

Split it into 3s as much as possible, and if you have 4 left, it will become two 2s

The maximum is 3 9 x 2 2

Because 31 itself is a prime number, you can only find a prime number smaller than thirty-one, and the answer is; 29*2

Split 37 into several different prime numbers.

The sum of the multiplication, how many scattered infiltration with a few different dismantling fingering?

There are 10 kinds, 37=3+5+29, 37=2+5+7+23, 37=3+11+23, 37=2+3+13+19, 37=5+13+19, 37=7+11+19, 37=2+5+11+19, 37=7+13+17, 37=2+5+13+17, 37=2+7+11+17, a total of 10 different dismantling methods

0 species. In other words, this question is wrong, the reason is: 35 is an odd number, and if it is to be broken into the sum of the two previous numbers, it can only be an even number and an odd number.

Only 2 in even numbers is prime. And 2+33=35, but 33 is not a prime number.

Therefore, there is no solution to this problem.