Mathematics
The problem that hasn’t been solved in 280 years…
Even after 280 years of its existence this math problem has yet to be solved.
One of oldest unsolved problems in number theory and one of the most well-known problems in all of mathematics. This hypothesis was initially put out in a letter from the Russian mathematician Christian Goldbach to the Swiss mathematician Leonhard Euler in 1742. And yet even though it was made so long ago and despite considerable effort the problem has yet to be solved.
The official name of this hypothesis is named “Goldbach’s Conjecture.” This conjecture states that every even natural number that is greater than 2 is the sum of two primes.
Examples
A prime number is a number that can only be divided by itself and 1. As an example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc. 1 can only be divided by itself so it is not a prime number. But back when the conjecture was first thought out the number 1 was considered a prime number. With that all prime numbers, with the exception of 2, are all odd numbers.
A demonstration of Goldbach’s Conjecture:
4 = 2 + 2
6 = 3 + 3
8 = 5 + 3
10 = 7 + 3 or 5 + 5
12 = 5 + 7
Trying to solve the Goldbach Conjecture
For the past 280 years have tried to prove or disprove the conjecture without any success. Before advancements in technology happened such as computers mathematicians would have to hand write and laboriously check prime numbers and even numbers by hand. Even doing this just by hand, the conjecture was proven true for the first numbers up to 100,000 in 1938 by Nils Popping.
But now that we have made computers that can repeat functions and check instantly with the use of programming and massive supercomputers we can check for much much bigger numbers.
Using those supercomputers the Goldbach Conjecture has been proven true for every single even number from zero to 1⁰¹⁸. That is 4 quintillion. Which is 4 MILLION TRILLIONS. An incredibly massive number. However, even though the conjecture has been proven true for every even number up to 4 quintillion this does NOT prove nor disprove Goldbach’s Conjecture. It is still very much possible that there is an even number that is not the sum of 2 prime numbers. And there is yet to be mathematical proof that this conjecture is true for all even numbers.
Goldbach’s Comet
Goldbach’s Comet is pretty much another branch of Goldbach’s Conjecture that shows the amount of times in which each even number up to a million can be expressed as the sum of two primes.
It looks kind of like this.
The y-axis represents g(E) which is the even number. And the x-axis the amount prime numbers can add up to the g(E). Which is usually represented by n. As an example, g(10) = 2 because it can be expressed as the sum of 2 primes in 2 different ways(10 = 5 + 5, 10 = 7 + 3).
Conclusion:
The Goldbach Conjecture was initially proposed by Christian Goldbach in 1742 and nearly 300 years later it has yet to be proven or disproven. Even with supercomputers, 100’s of mathematicians working on it for years and countless functions trying to solve it, it has yet to be solved 280 years later.
