The Goldbach Conjecture

This conjecture states that every even integer greater than 4 can be expressed as the sum of two odd primes. Alternatively, another form of the conjecture states that every even integer greater than two can be expressed as the sum of two primes.

In a letter to Leonhard Euler in the year 1742, Christian Goldbach hazarded the guess as follows:

Every integer which can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until all terms are units.

But you should note that he believed 1 to be a prime number. So, here, the primes include 1.