Goldbach Conjecture/Historical Note

Conjecture

Christian Goldbach actually proposed what is now known as Goldbach's Marginal Conjecture in $1742$ in a letter to Leonhard Paul Euler. Euler then proposed this stronger conjecture.

It was published in Edward Waring's Meditationes Algebraicae of $1770$.

It has been checked by computer for numbers up to at least $10^{18}$.


In $1937$ Ivan Matveevich Vinogradov proved Vinogradov's Theorem: that all sufficiently large odd numbers are the sum of $3$ primes.

In $1973$ Chen Jingrun proved Chen's Theorem: that every sufficiently large even number is the sum of a prime and either another prime or a semiprime.

In $1995$ Olivier Ramaré showed in Ramaré's Theorem that every even number is the sum of no more than $6$ primes.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Goldbach's conjecture
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Goldbach's conjecture
  • 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Fermat
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