Find Three Prime Numbers by Sum Calculator

Welcome to the free online calculator to find three prime numbers by a given sum. For example, if the sum of three prime numbers is 235, what are the prime numbers?

Find Three Prime Numbers by Sum Calculator

Eg, what are three prime numbers whose sum is 235? Enter 235 in the input box, then click Calculate button.

Calculate Reset

How to find three prime numbers based on a given sum

First, what are prime numbers?

A prime number is a natural number greater than 1 with no factors other than 1 and itself. Prime and Composite Number Checker help you quickly verify prime numbers.

So, how to find three prime numbers by a given sum?

This is a very tricky question. First, find all prime numbers from 1 to the sum. Then, calculate whether the sum of the three prime numbers is equal to the sum. As you can imagine, it took a lot of work to find the answer.

For example, What three prime numbers sum up to 12?

First, find all prime numbers from 1 to 12. There are a total of 5 prime numbers:

2, 3, 5, 7, 11

Second, calculate the sum of three prime numbers, 5 prime numbers share 10 combinations, which are:

2 + 3 + 5 = 10

2 + 3 + 7 = 12

2 + 3 + 11 = 16

2 + 5 + 7 = 14

2 + 5 + 11 = 18

2 + 7 + 11 = 20

3 + 5 + 7 = 15

3 + 5 + 11 = 19

3 + 7 + 11 = 21

5 + 7 + 11 = 23

So, the three prime numbers are 2, 3 and 7.

Is it troublesome? There are 10 combinations of only 5 prime numbers under the sum. If there are 10 prime numbers there are 120 possibilities. Imagine, if you wanted to calculate the sum of three prime numbers is more than 1000. What should you do? It can’t be solved by manual calculation at all.

Therefore, you desperately need a helper tool to do the job. Find Three Prime Numbers by Sum Calculator is designed to solve such problems, the calculator omits all steps and gives the answer in milliseconds.

Other tools find two prime numbers by a given sum.

Next, we will introduce how to use the calculator.

How to use the calculator to find two prime numbers

Using the calculator is simple, follow these 2 steps:

1Enter the sum in the input box.
2Click Calculate button to get the answer, or click Reset button to start a new calculation.

Next, let’s look at some examples.

Solved examples using the find three prime numbers by sum calculator

Example 1: What are three prime numbers whose sum is 100?

Enter 100 in the input box.

Then click Calculate button, as shown in the figure, the three prime numbers are (2, 19, 79) or (2, 31, 67) or (2, 37, 61).

2 + 19 + 79 = 100

2 + 31 + 67 = 100

2 + 37 + 61 = 100

What are three prime numbers whose sum is 100?

Example 2: What are three prime numbers whose sum is 173?

Enter 173 in the input box.

Then click Calculate button, as shown in the figure, there are 80 possible combinations of 3 prime numbers that add up to 173

(3, 7, 163)

(3, 13, 157)

(3, 19, 151)

(3, 31, 139)

(3, 43, 127)

(3, 61, 109)

(3, 67, 103)

(3, 73, 97)

(5, 11, 157)

(5, 17, 151)

(5, 19, 149)

(5, 29, 139)

(5, 31, 137)

(5, 37, 131)

(5, 41, 127)

(5, 59, 109)

(5, 61, 107)

(5, 67, 101)

(5, 71, 97)

(5, 79, 89)

(7, 17, 149)

(7, 29, 137)

(7, 53, 113)

(7, 59, 107)

(11, 13, 149)

(11, 23, 139)

(11, 31, 131)

(11, 53, 109)

(11, 59, 103)

(11, 61, 101)

(11, 73, 89)

(11, 79, 83)

(13, 23, 137)

(13, 29, 131)

(13, 47, 113)

(13, 53, 107)

(13, 59, 101)

(13, 71, 89)

(17, 19, 137)

(17, 29, 127)

(17, 43, 113)

(17, 47, 109)

(17, 53, 103)

(17, 59, 97)

(17, 67, 89)

(17, 73, 83)

(19, 23, 131)

(19, 41, 113)

(19, 47, 107)

(19, 53, 101)

(19, 71, 83)

(23, 37, 113)

(23, 41, 109)

(23, 43, 107)

(23, 47, 103)

(23, 53, 97)

(23, 61, 89)

(23, 67, 83)

(23, 71, 79)

(29, 31, 113)

(29, 37, 107)

(29, 41, 103)

(29, 43, 101)

(29, 47, 97)

(29, 61, 83)

(29, 71, 73)

(31, 41, 101)

(31, 53, 89)

(31, 59, 83)

(37, 47, 89)

(37, 53, 83)

(41, 43, 89)

(41, 53, 79)

(41, 59, 73)

(41, 61, 71)

(43, 47, 83)

(43, 59, 71)

(47, 53, 73)

(47, 59, 67)

(53, 59, 61)

What are three prime numbers whose sum is 173?

Find Three Prime Numbers by Sum Calculator