In 1742, Christian Goldbach, math tutor to Tsar Peter II, guessed that any even number greater than two can be written as the sum of two prime numbers. (Prime numbers are those…

In 1742, Christian Goldbach, math tutor to Tsar Peter II, guessed that any even number greater than two can be written as the sum of two prime numbers. (Prime numbers are those that can be divided only by themselves or 1.) Thus, for example, 24 is the sum of 11 and 13. While it's easy to take an individual number and figure out what two primes you need--computers have done this for all even numbers up to 400 trillion--it's incredibly difficult to prove that Goldbach's guess holds true for all of the infinite host of even numbers. Chinese mathematician Chen Jing-Run has come the closest so far; he proved that any even number is equal to a prime plus the product of two primes. (Take 24 again: It can be represented as 3 + 21, which is 3 × 7.) But close isn't good enough in mathematics, so the original conjecture remains unproven.