Ask A Scientist Mathematics Archive

Author:      jonathan j hoch
What is the Goldbach Conjecture?

Response #:  1 of 2
Author:      asmith
That every even number is the sum of two prime numbers.


Response #:  2 of 2
Author:      tee
Christian Goldbach (1690-1764), in a letter to Euler dated February, 16,
1745, stated that every even number equal to or greater than 6 is the sum of
two odd primes in one or more ways.  The first sentence is a direct quote
from THE LORE OF PRIME NUMBERS by G. P. Loweke, p 68.  The conjecture
remains unsettled, but computers have verified the conclusion for all even N
below very large bounds (Loweke noted the bound of 100,000 but that is quite
old, I believe).  A related conjecture is that every even number is a
difference of two primes in infinitely many ways!  Loweke ascribes this
statement to A. de Polignac around 1849.