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 generating a list of prime numbers. Then, we check each integer starting from 2 to see if it can be expressed as the sum of two or more different primes.
Here's an example algorithm to find the largest integer:
1. Generate a list of prime numbers up to a certain limit. This limit can be arbitrarily chosen based on the range of integers you want to consider.
- One way to generate prime numbers is by using the Sieve of Eratosthenes algorithm. It involves initializing an array of all numbers from 2 to the desired limit, then iteratively marking multiples of each prime number as composite (not prime).
2. Starting from 2, check if each integer can be expressed as the sum of two or more different primes.
- For each number, iterate through the list of prime numbers and check if the difference between the current number and each prime is also a prime number. If it is, then the current number can be expressed as the sum of two different primes.
3. Keep track of the largest number that cannot be expressed as the sum of two or more different primes.
- Initialize a variable to hold the largest number found so far. Update it whenever a larger number is found that cannot be expressed as the sum of two different primes.
4. Repeat step 2 and 3 until all numbers have been checked.
At the end, the value stored in the variable representing the largest number found will be the answer.
Note: This algorithm might take some time to run, especially if searching for large numbers or using a large prime number limit. However, it guarantees to find the largest integer that meets the criteria.