the largest integer that is not the sum of two or more different primes
My guess would be 3 if I interpret your question correctly.
To find the largest integer that is not the sum of two or more different primes, you can approach it by considering prime numbers and consecutive integers.
First, let's start by listing some prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on.
Next, let's consider consecutive integers and add up the prime numbers to check if any of them can be formed as a sum.
Starting with 2, we can create sums like 2 = 2 (which is already a prime) or 2 + 2 = 4 (which is not a prime).
Moving on to 3, we can create sums like 3 = 3 (already a prime), but we cannot create any other sums from consecutive integers, as 3 is the next prime number.
Next, with 5, we can have 5 = 5, 5 + 5 = 10, 5 + 5 + 5 = 15, and so on. But if we keep going, eventually we'll reach a sum that is not a prime, for example:
5 + 5 + 5 + 5 + 5 + 5 = 30 (not a prime)
By this process, we can see that 29 is the largest prime number that cannot be expressed as the sum of two or more different primes.
So, the answer to your question is 29.