# What numbers can be written as the sum of three prime numbers?

## What numbers can be written as the sum of three prime numbers?

Every integer greater than 2 can be written as the sum of three primes. He considered 1 to be a prime number, a convention subsequently abandoned. So today, Goldbach’s original conjecture would be written: Every integer greater than 5 can be written as the sum of three primes.

### How do you express a number as a sum of prime numbers?

There are two ways to write either 5 or 6 as sums of primes: 5 = 5 and 5 = 2 + 3, as well as 6 = 3 + 3 and 6 = 2 + 2 + 2. For the number 7 we get three ways: 7 = 7, 7 = 5 + 2 and 7 = 3 + 2 + 2. After that things gain a bit of momentum, and e.g. for N = 17 there are 17 ways to write it as a sum of primes.

#### How many ways can 50 be written as the sum of two prime numbers?

four different ways
For example, we can write N = 50 as the sum of two primes in four different ways: 50 = 3+47 = 7+43 = 13+37 = 19+31.

Can the sum of three prime numbers be a prime number?

It has long been conjectured that every odd number greater than 7 is the sum of 3 primes. It is known that every large enough odd number is the sum of three primes. I do not know of any extra information known if the target odd number is itself prime.

Can a number be expressed as a sum of two prime numbers?

20 can be expressed as sum of two prime numbers 3 and 17, 13 and 7.

## Can a prime number be expressed as a sum of two prime numbers?

Every integer that can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until all terms are units. Every positive even integer can be written as the sum of two primes. This is in fact equivalent to his second, marginal conjecture.

### What is sum prime number?

How to find the sum of prime numbers up to a prime number n, that is for example: the sum of prime numbers up to 7 is: 2+3+5+7=17.

#### How many ways can 40 be expressed as the sum of two prime numbers?

Two prime numbers that add up to 40 are 3 and 37, but they also can be 11 and 29 as well as 17 and 23.

How many ways can 24 be written as the sum of two different prime number?

There are exactly 3 ways of expressing 24 as the sum of two prime numbers.

Which is the sum of all prime numbers up to 45?

Below are the prime numbers up to 45 that can be expressed as sum of consecutive prime numbers: 5 = 2 + 3 17 = 2 + 3 + 5 + 7 41 = 2 + 3 + 5 + 7 + 11 + 13

## How many ways can a number be expressed as a sum?

All the positive numbers can be expressed as a sum of one, two or more consecutive positive integers. For example 9 can be expressed in three such ways, 2+3+4, 4+5 or 9.

### How to find the sum of all primes?

Initialize sum as the smallest prime found i.e., element at index 0 in the vector. Iterate over the range [1, X – 1] and add each element to the sum. After adding, check if the sum is a prime or not and the sum is less than N or not.

#### How many ways can a number be represented?

The number of ways of representing a number by consecutive integers is equal to the number of divisors of the largest odd divisor of that integer minus 1. (If you count the number itself as a representation, you don’t need to subtract 1). The number of divisors of a number n = pa11 pa22… pakk, is d(n) = (a1 + 1)(a2 + 1)… (ak + 1).