number theory

Goldbach’s Conjecture

umasundresh 8 Oct 2021 No Comments

Any even number greater than 2 can be written as the sum of two prime number.

Every odd whole number greater than 5 can be written as the sum of three primes. 

Goldbach’s conjectures

Goldbach, a Prussian mathematician(1690-1764)

On 7 June 1742, Goldbach wrote a letter to the mathematician Euler in which he proposed the conjectures he found.

Euler responded back on 30 June 1742 as

Every integer greater than 2 is a sum of two primes, I regard this as a completely certain theorem, although I cannot prove it.

Euler

Though the Goldbach’s conjecture looks simple to understand, it has not yet been proved.

In the modern times, the conjectures proposed by Goldbach is identified as weak or strong Goldbach conjecture.

In 2013, Harold Helfgott, a Peruvian mathematician released two papers claiming the proof of Goldbach weak conjecture and The proof was accepted for publication in the Annals of mathematics series in 2015, and has been undergoing further review and revisions.

In March 2000 the publishers of the book ‘Uncle Petros and Goldbach’s conjecture (Bloomberg in the USA and Faber and Faber in the UK) offered a prize of one million dollars for anyone who could prove the Goldbach’s conjecture

Any even whole number greater than 2 can be written as the sum of two prime number.

The prize was kept open for two years, but nobody claimed it.