 The Strong Goldbach Conjecture is a yet unproven theory stating that 'every even integer greater than two is the sum of two prime numbers'. For example:The Prussian mathematician Christian Goldbach originally proposed a similar theory in 1742: 'Every integer greater than 5 can be written as the sum of three primes'. This is known as the 'ternary' or 'weak' Goldbach conjecture. The famous mathematician Leonhard Euler a few years later modified the theory to it's present form, called the 'Strong Goldbach Conjecture': Neither Euler, nor anyone else in the almost three centuries since, has been able to prove it. Goldbach's conjecture is one of the oldest unsolved problems in all of mathematics. For small even numbers, the Goldbach conjecture can be verified directly. It's pretty easy to do. 146, for instance, is 139 + 7. The tricky part is checking to see if both values are prime numbers. There's a prime number checker on our prime numbers page that makes this easy. In 1938, Nils Pipping laboriously verified the conjecture up to 100,000. Without a calculator! With the advent of computers, many more values have been checked. As of 2013, even numbers up to up to 4×1018 (4,000,000,000,000,000,000) have been checked. However, all this shows is that the conjecture is true for all even numbers less than that. It is possible that there exists an even larger number which cannot be split into two primes. What has never been found is a mathematical proof that the conjecture is true for all even numbers. In March 2000 the publishers of a book about the conjecture offered a prize of one million dollars to anyone who could prove the Goldbach conjecture and whose proof was accepted by fellow mathematicians. The prize was kept open for two years but nobody claimed it. |