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 prime numbers and calculating their sums:
2 = 2
3 = 3
5 = 2 + 3
7 = 7
11 = 2 + 3 + 5 + 11
...
As we continue listing out prime numbers and calculating their sums, we eventually reach a point where we are unable to express an integer as the sum of different primes. This largest integer is known as the Goldbach's weak conjecture.
Goldbach's weak conjecture states that every odd integer greater than 5 can be expressed as the sum of three prime numbers. However, this conjecture has not been proven, so we cannot definitively say that there is a largest integer that cannot be expressed as the sum of two or more different primes.
Nonetheless, mathematicians have made extensive computational efforts to test Goldbach's weak conjecture for large numbers. As of now, no counterexamples have been found. However, due to its unproven nature, we cannot claim with certainty that there is a largest integer that cannot be expressed as the sum of two or more different primes.