@Mictorrani
edited
The Goldbach Conjecture
Since Andrew Wiles and Richard Taylor were finally able to devise a proof of Fermat's last Theorem in the mid-1990s, the most famous unsolved mathematical problem might very well be proving the Goldbach conjecture. It was proposed by Russian mathematician Christian Goldbach (1690-1764) in a correspondence with Leonhard Euler (1707-1783) in 1742. Goldbach claimed that ***every number greater than 2 is an aggregate of three prime numbers***. The modern version of the conjecture states that ***every even natural number greater than 2 is equal to the sum of two prime numbers.*** (In order to get from the first version to the second, remove the third prime, namely 1, which was considered a prime in Goldbach's time but is not included in the definition of a prime number any longer. By removing 1, we also remove the odd numbers from the discussion. The two versions are equivalent, since every odd number greater than 1 is a sum of an even number and 1.) The conjecture has been verified by computation for numbers from 4 to 400,000,000,000,000, but no one has so far been able to prove its generality by formal mathematical methods. Chinese mathematician Chen Jing Run has been able to prove that ***every sufficiently large even number is the sum of a prime and a number with at most two prime factors,*** but that doesn't prove the Goldbach conjecture For readers being unaccustomed to the language used in mathematics, let's see by a few examples what it means that an even natural number greater than 2 is equal to the sum of two prime numbers. 8 is the sum of 3 and 5, two primes. 12 is the sum of 5 and 7. 20 is equivalent to 17+3, two prime numbers. It can even be done in two ways, because the sum of two other primes, 13 and 7, is also 20. (This material has previously been published in TMA/Meriondho Leo and in my e-book “Numericon”.) Copyright © 2019, 2020 Meleonymica/Mictorrani. All Rights Reserved. If you are interested in numbers, you find all my articles related to numbers here, and please also join my community Numbers (7b6a). https://read.cash/@Mictorrani/index-over-my-articles-at-read-cash-5f7c1e34#numbers https://read.cash/c/numbers-7b6a You find all my writings on Read.Cash, sorted by topic, here. https://read.cash/@Mictorrani/index-over-my-articles-at-read-cash-5f7c1e34
9 comments
You have made something potentially complicate to understand, very clear. Thank you.
I'm very glad to hear that, because that is exactly what I tried to do. Then I was successful.
12+8 = 20 too so is 1 + 19 and 4+16 but that doesn't mean if you are not into maths your article makes clear what you are talking about.
I was talking about the sum of two prime numbers. You are not. Prime numbers lower than 20 are 2, 3, 5, 7, 11, 13, 17 and 19.
That is exactly my point. Your article doesn't make any sense to someone who isn't into maths.
Ok, it may be so, but it makes sense to those who are.
Am not really a maths person but I think i can get alittle of what you solved in your article. Nice calculations, you must really good at maths
Thanks. It's good if you can understand something of it even without being a maths person. Then I have managed to explain it clearly. I appreciate very much to hear that.
Maths can be a lot of fun. Just pick up some new stuff every week, and you will accumulate more abilities in this area and increase your interest.