Goldbach's first conjecture

jomlau 08 Sep 2008 17:47

I took a look at the Wikipedia page for Goldbach's conjecture and found some interesting things. Originally, Goldbach proposed to Euler that every number greater than 2 could be expressed as a sum of three primes, back when 1 was considered to be a prime; a modern version of this would be every number greater than 5.

Looking at even numbers, we need either to sum three even numbers or two odd numbers with an even number. The only number that matches the former description is 6 = 2 + 2 + 2. As for the latter, we can see that this boils down to the Goldbach's conjecture that we know today; the even number must be 2, forcing us to find two odd primes that add up to an even number.