the largest integer that is not the sum of 2 or more different primes.
To find the largest integer that is not the sum of 2 or more different primes, we can start by recognizing that any even number greater than 2 can be expressed as the sum of two prime numbers (this is known as Goldbach's Conjecture). Therefore, we need to focus on odd numbers.
We can start by listing the first few odd prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and so on.
To find the answer, we can work our way up from the largest odd number and check if it can be expressed as the sum of two or more different prime numbers. Let's start with 47:
47 = 13 + 17 + 19
47 = 3 + 13 + 31
As we can see, 47 can be expressed as the sum of different prime numbers.
Now, let's move on to the next odd number, which is 45:
45 = 5 + 17 + 23
Since we found a way to express 45 as the sum of different prime numbers, it is not the largest integer that meets our criteria.
Continuing this process, we move on to 43:
43 = 2 + 41
We found a way to express 43 as the sum of different prime numbers.
Now, let's move on to the next odd number, which is 41.
41 = 41
In this case, we can express 41 as the sum of one prime number, which is itself. However, since this question asks for the largest integer that is not the sum of 2 or more different prime numbers, we can conclude that it is the largest such integer. Therefore, the largest integer that is not the sum of 2 or more different primes is 41.
To summarize, we worked our way up from the largest odd numbers and checked if they can be expressed as the sum of two or more different prime numbers until we found a number that cannot be expressed this way, which is 41.