A Goldbach number is an even positive integer that can be expressed as the sum of two primes. Therefore, another statement of Goldbach's conjecture is that all even integers greater than or equal to 4 are Goldbach numbers.
The expression of a given even number as a sum of two primes is called a Goldbach partition of that number. For example:
- 2(2) = 4 = 2 + 2
- 2(3) = 6 = 3 + 3
- 2(4) = 8 = 3 + 5
- 2(5) = 10 = 3 + 7 = 5 + 5
- ...
- 2(50) = 100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53
- ...
The number of unordered ways in which 2n can be written as the sum of two primes (for n starting at 1) is:
- 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, ... ( A045917).
Read more about this topic: Goldbach's Conjecture
Famous quotes containing the word number:
“My idea is that the world outside—the so-called modern world—can only pervert and degrade the conceptions of the primitive instinct of art and feeling, and that our only chance is to accept the limited number of survivors—the one- in-a-thousand of born artists and poets—and to intensify the energy of feeling within that radiant centre.”
—Henry Brooks Adams (1838–1918)