Goldbach conjecture

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Goldbach's conjecture states, that every even integer greater than 2 can be expressed as the sum of two primes.

You can tell from small numbers, because

  4 = 2 + 2
  6 = 3 + 3
  8 = 3 + 5
10 = 3 + 7 = 5 + 5
  ⋮
100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53

No one knows if this always goes on. It is one of the oldest unproven statements in number theory and in all of mathematics.

The conjecture was expressed in a letter Christian Goldbach wrote to Leonhard Euler in 1742.