The largest integer that is not the sum of two or more different primes?
To find the largest integer that is not the sum of two or more different primes, we can start by listing out the primes and calculating their sums.
The first step is to generate a list of prime numbers. We can do this by using a prime number generator algorithm, such as the Sieve of Eratosthenes. Let's generate primes up to a certain limit (let's say 100) to have a range to work with.
Using the Sieve of Eratosthenes:
1. Start with a list of all numbers from 2 to the limit (100 in this case).
2. Mark the first number (2) as prime.
3. Cross out all multiples of the current prime number (2), leaving only the prime number itself.
4. Move to the next unmarked number (3) and mark it as prime.
5. Cross out all multiples of the current prime number (3), leaving only the prime number itself.
6. Repeat steps 4 and 5 until all numbers up to the limit have been considered.
Following this algorithm, we can generate a list of primes up to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Next, we can calculate the sums of these prime numbers. Starting from the smallest prime (2), we add it with other primes and write down the sums.
2 + 3 = 5
2 + 5 = 7
2 + 7 = 9
...
2 + 97 = 99
Then we move to the next prime (3) and repeat the process.
3 + 5 = 8
3 + 7 = 10
3 + 11 = 14
...
3 + 97 = 100
We continue this process for each prime number, writing down all the non-repeated sums.
Finally, we look at the list of sums and find the largest integer that does not appear. In this case, the largest integer that is not the sum of two or more different primes is 98.
Therefore, the answer to your question is 98.