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Goldbachs conjecture

Goldbachs conjecture

Goldbach conjecturte is one of the best known unsolved mathematical problem in number theory.

Modern version of Goldbach marginal conjecture is defined as

Every integer greater than five is the sum of three prime numbers. Examples are,

5 = 3 + 1 + 1

6 = 3 + 2 + 1

7 = 5 + 1 + 1

8 = 5 + 2 + 1

Goldbach original conjecture is defined as

Every even integer greater than two is sum of two prime numbers. So all even integers greater than two are considered to be Goldbach numbers.

The expression of even number as sum of two prime numbers is called as Goldbach partition.

Few examples of Goldbach partition of original conjecture are

4 = 2 + 2

6 = 3 + 3

8 = 5 + 3

10 = 5 + 5...

All odd numbers greater than 7 are the sum of three odd primes, this conjecture is called to be the weak or odd or ternary Goldbach conjecture.

This conjecture was written by German mathematician Christian Goldbach to the Leonard Euler in 1742. The weak conjecture was proved to be true in 2013. While the strong conjecture has been shown to hold up through 4 - 1018 ,but it is not yet resolved. If the strong conjecture proved to be true than the weak conjecture will also be true based on the conclusion.

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