In June of 1742, Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (the mathematician so influential that they named a number after him) in which he laid out this famous conjecture. It was refined a bit since that fateful day to say this: All even whole numbers greater than two are the sum of two prime numbers.

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A prime number, to refresh your memory, is a number that can only be divided by 1 and itself. Let's try out the conjecture on the even number 4. 4 can be expressed as 2 + 2. 2 is a prime, so the conjecture holds up. Same goes for a larger number like 28. You can express 28 as the sum of the prime numbers 5 and 23, or 11 and 17. You can go even higher—why not try something crazy like 12,345,678? That can be expressed as the sum of prime number 20,297 and 12,325,381. (You can try it yourself on this Goldbach calculator.) Hey, that all worked! We did it. A nearly 300-year-old math problem solved right here, right now. Well, not so fast.