Goldbach's original conjecture (known as the "ternary" Goldbach conjecture) was stated in a letter he wrote to Euler in 1742:

Every number that is greater than 2 is the sum of three primes -- Christian Goldbach

In this case he was treating the number 1 as a prime number but we no longer follow that convention today. Euler re-stated it in the more familiar form now known as the "binary" or "strong" Goldbach conjecture:

All positive even integers greater than 2 can be expressed as the sum of two primes -- Euler, restating Goldbach's conjecture

The conjecture can be written algebraically as follows:

2n = p + q

p + q n = ----- 2

Here,andare both primes numbers.is a natural (whole) number, andis therefore an even number. If we divide both sides of the equation by 2, we get the following:

So another way of expressing Goldbach's conjecture is as follows:

Every integer greater than 1 is the average of two prime numbers. -- Wardley, restating Euler restating Goldbach

Despite being over 250 years old, Goldbach's conjecture remains unproven. It has been tested for the first few billion numbers and no-one has ever found a counter-example. Most mathematicians believe it to be true, but no-one has ever proved it. And so it remains a conjecture.