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- Every integer greater than 2 can be written as the sum of three primes.
He considered 1 to be a prime number, a convention subsequently abandoned. A modern version of Goldbach's original conjecture is:
- Every integer greater than 5 can be written as the sum of three primes.
Euler, becoming interested in the problem, answered by noting that this conjecture would follow from a stronger version,
- Every even integer greater than 2 can be written as the sum of two primes,
adding that he regarded this a fully certain theorem ("ein ganz gewisses Theorema"), in spite of his being unable to prove it.
- Goldbach's conjecture, part of Chris Caldwell's Prime Pages.