Goldbach's conjecture facts for kids
Goldbach's conjecture is one of the oldest and most famous unsolved puzzles in mathematics. It's a big mystery that mathematicians have been trying to solve for hundreds of years! It's all about even numbers and prime numbers.
The conjecture says that every even integer (a whole number) greater than 2 can be written as the sum of two primes.
For example:
- 4 = 2 + 2
- 6 = 3 + 3
- 8 = 3 + 5
- 10 = 3 + 7 (or 5 + 5)
- 20 = 3 + 17 (or 7 + 13)
- 100 = 3 + 97 (or 11 + 89, or 17 + 83, and many more!)
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, and so on. Numbers like 4 (which can be divided by 2) or 6 (which can be divided by 2 and 3) are not prime.
Contents
How the Conjecture Started
The idea for Goldbach's conjecture came from a letter written on 7 June 1742. A Prussian mathematician named Christian Goldbach sent this letter to another famous mathematician, Leonhard Euler.
In his letter, Goldbach suggested a conjecture (which is like a mathematical guess or statement that seems true but hasn't been proven yet). This statement is now called Goldbach's strong conjecture.
Goldbach's Original Idea
Goldbach's original idea was a bit different from what we know today. He thought that every whole number greater than 2 could be written as the sum of two prime numbers. At that time, some mathematicians, including Goldbach, considered the number 1 to be a prime number. Today, mathematicians do not consider 1 to be a prime number.
The Weak Conjecture
Goldbach also had a slightly different version of his idea, which is called Goldbach's weak conjecture. This version states:
- Every integer greater than 5 can be written as the sum of three primes.
When Euler received Goldbach's letter, he became very interested in the problem. He wrote back to Goldbach, saying that if Goldbach's strong conjecture was true, then the weak conjecture would also be true. Euler felt very sure that the strong conjecture was correct, but he couldn't find a way to prove it.
What Happened Next
For centuries, mathematicians have tried to prove Goldbach's strong conjecture, but no one has succeeded yet. It remains one of the biggest unsolved problems in number theory.
However, Goldbach's weak conjecture was finally proven! In 2013, a mathematician named Harald Helfgott successfully showed that it is true. This was a huge step forward in understanding these famous conjectures.
Even though the weak conjecture is solved, the strong conjecture is still waiting for someone to find its proof.
Images for kids
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This graph shows how many different ways an even number n (from 4 up to 1,000,000) can be written as the sum of two primes.
See also
In Spanish: Conjetura de Goldbach para niños
