Breakthrough for 270-year old mathematics riddle

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16 mei 2012 | The American researcher Terence Tao brought the world closer to proving a 270 year old mathematical riddle. He allegedly showed with a general proof that every uneven integer larger than 1 can be expressed as the sum of three prime numbers. A breakthrough also for cryptography and banking?

Terence Tao from the University of California in Los Angelespublished a paper elaborating on a general proof that everyinteger larger than 1 can be expressed as the sum of three primenumbers. The paper, which is yet to undergo an extensivepeer-review, would as such be a major breakthrough towards a prooffor the Goldbach conjecture.

In 1742, the mathematician Christian Goldbach wrote a letter tohis famous colleague Leonard Euler where he put forward theconjecture that every uneven integer larger than 5 can be dividedinto 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 missingso far. Apart from sparking great interest from a scientific pointof view, research in prime numbers could lead to meaningfuladvancements in cryptography.

Internet banking for instance employs the so-called RSA method. Through this a ‘public key’ iscreated which is the product of two extremely large prime numbers,both between 150 and 300 digits. To decipher this code, a privatekey (the two prime numbers) is needed which is given to thecustomer.

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