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'Goldbach's conjecture'
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| Title of object: |
Goldbach's conjecture |
| Canonical Name: |
GoldbachsConjecture |
| Type: |
Conjecture |
| Created on: |
2002-01-24 11:25:38 |
| Modified on: |
2002-12-28 14:43:17 |
| Classification: |
msc:11-00, msc:11P32 |
Revision comment (for changes between this and next version):
| Changes for correction #10579 ('capitalization'). |
Preamble:
Content:
The conjecture states that every even integer $n>2$ is expressible as the sum of two primes.
In 1966 Chen proved that every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime divisors.
Vinogradov proved that every sufficiently large \emph{odd} number is a sum of three primes. In 1997 it was shown by J.-M. Deshouillers, G. Effinger, H. Te Riele, and D. Zinoviev that assuming Generalized Riemann Hypothesis every odd number $n>5$ can be represented as sum of three primes.
The conjecture was first proposed in a 1742 letter from Christian Goldbach to Euler and still remains unproved. |
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