the goldbach conjecture is that every even number that is greater than 2 can be shown as the sum of two prime numbers. some examples are shown below:
- 4 = 2 + 2
- 6 = 3 + 3
- 8 = 3 + 5
- 10 = 3 + 7
The Goldbach Conjecture is one of the oldest unsolved problems in number theory. It was proposed by the Prussian mathematician Christian Goldbach in 1742.
The conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. So far, extensive computational testing has been conducted, and no counterexample has been found.
However, the Goldbach Conjecture remains unproven. Despite numerous attempts by mathematicians over the centuries, a general proof for all even numbers is yet to be discovered. A partial result in this direction, known as the strong Goldbach conjecture, states that every odd number greater than 5 can be expressed as the sum of three prime numbers.
Although the conjecture has not been proven, it has held true for a vast range of even numbers up to very large values. Intensive research and significant progress continue to be made towards proving or disproving the Goldbach Conjecture.
That's correct! The Goldbach Conjecture states that every even number greater than 2 can be expressed as the sum of two prime numbers.
Here are a few more examples:
- 12 = 5 + 7
- 14 = 3 + 11
- 16 = 3 + 13 or 5 + 11
- 18 = 5 + 13 or 7 + 11
While the Goldbach Conjecture has been tested extensively for even numbers up to very high values, it has not been proven or disproven for all even numbers.