Longest Mathematical Problem
By: Andrei Tapalaga
Tags: Math, Mathematics, World, Problems, History

Longest Mathematical Problem

Dating back to 1742

Christian Goldbach

A Russian Mathematician by the name of Christian Goldbach has come up with the longest mathematical problem the world has ever seen. Many historians do not talk about this as there is very little proof to justify that he had been the sole creator of this formula apart from his Profession diplomas as well as many years of study. He was nominated as the best mathematician in Russia in 1975 as his brilliant mind could any problem that was given to him. This is what made him want to create a challenge, not only for himself but for those who were going against him at the title of world lead mathematician.

In his new problem that would be a great challenge, Goldbach states that every even positive integer greater than 3 is the sum of two primes. For 257 years no one has succeded in proving or disapproving the validity of Goldbach’s conjecture. As mentioned in one of my previous articles, maths does not always have the right logic. The conjecture has presented itself to hold for all integers less than 4 times 10 to the power of 18 but still remains unproven despite enormous efforts from leading mathematicians around the world.

Even Albert Einstein had a crack at this problem but it was futile, every way that he would approach the conjecture it would prove futile. We need a millennial to crack this one.

There has been some sort of document discovered under the name of Goldbach trying to better yet explain the problem he has come up with. So apparently the expression of a given even number as a sum of two prime numbers called a Goldbach partition of that number. These are some of Goldbach’s partitions for even numbers:

6=3+3

8=3+5

10=3+7=5+5

12=7+5

Onward to something as

100=3+97=11+89=17+83=29+71=41+59=47+53

There are many other technical calculations that go into solving this problem or at least attempting to solve this problem but, this is so you get the gist.

The last document that was found under his name was a letter from him to Euler Leonhard dating back to 7 of June 1742 in which a fellow mathematician to whom he has proposed the following conjecture:

“ Every integer that can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes until all terms are units.”

On the Margin of the letter, he has proposed a second conjecture.

“Every integer greater than 2 can be written as the sum of three primes.”

A second document was a letter from Euler responding to his letter on the 30th of June 1742 stating in German the following.

“Dass … ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe nicht demonstriren kann.” (“That … every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it.”)

Some that have analyzed his work say that Euler has helped him to come up with the problem, however, there is very little documentation available on Euler Leonhard. No matter if this is true or not the problem still remains unsolved and a major problem that really makes you scratch your head is when you try to set n-3 as a sum of two prime numbers.

The problem at hand will still take lots of time and a next-level prodigy in maths to manage to solve this. It is not something that is impossible but certainly something that is of overwhelming demanding difficulty. I guess Goldbach has created the ultimate mathematical challenge.