Goldbach–Euler theorem

The conjecture that every even integer greater than 2 is the sum of two primes. It remains unproved and is usually called Goldbach’s conjecture.

Connect

Goldbach’s conjecture: The assertion that every even integer greater than 2 can be written as the sum of two primes. This is the standard modern name for the Goldbach–Euler theorem.
Christian Goldbach: An eighteenth-century Prussian mathematician whose correspondence with Euler introduced the conjecture’s precursor. His 1742 letter proposed the claim about expressing numbers as sums of primes.
Prime number: A natural number greater than 1 whose only positive divisors are 1 and itself. These are the permitted summands in the conjecture.
Riemann hypothesis: The conjecture that every nontrivial zero of the Riemann zeta function has real part one-half. Sharper control of primes from this hypothesis would improve some approaches to additive prime problems.
Weak Goldbach conjecture: The assertion that every odd integer greater than 5 is the sum of three primes. It replaces two prime summands with three and has been proved.
Leonhard Euler: An eighteenth-century Swiss mathematician whose work shaped number theory and mathematical analysis. His reply reformulated Goldbach’s proposal into the modern even-number conjecture.
Even number: An integer divisible by 2. The conjecture concerns every even integer greater than 2.
Twin prime conjecture: The assertion that infinitely many pairs of primes differ by 2. It is another famous unproved claim about how primes are distributed.
Goldbach’s comet: A graph of the number of ways each even integer can be expressed as a sum of two primes. Its rising, irregular counts visualize the conjecture’s representations.
Goldbach–Euler correspondence: The exchange of letters in which Christian Goldbach and Leonhard Euler discussed additive representations of integers by primes. The conjecture’s historical formulation emerged in this correspondence.