Terence Tao from the University of California in Los Angeles published a paper elaborating on a general proof that every integer larger than 1 can be expressed as the sum of three prime numbers. The paper, which is yet to undergo an extensive peer-review, would as such be a major breakthrough towards a proof for the Goldbach conjecture.
In 1742, the mathematician Christian Goldbach wrote a letter to his famous colleague Leonard Euler where he put forward the conjecture that every uneven integer larger than 5 can be divided into the sum of three prime numbers. For example:
13 = 5 + 5 + 3
27 = 13 + 7 + 7
Prime numbers key to cryptography
Despite this early discovery, a general proof has been missing so far. Apart from sparking great interest from a scientific point of view, research in prime numbers could lead to meaningful advancements in cryptography.
Internet banking for instance employs the so-called RSA method. Through this a 'public key' is created which is the product of two extremely large prime numbers, both between 150 and 300 digits. To decipher this code, a private key (the two prime numbers) is needed which is given to the customer.