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Goldbach’s conjecture

فبراير 19, 2012

Goldbach’s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer greater than 2 can be expressed as the sum of two primes.

The number of ways an even number can be represented as the sum of two primes

Goldbach’s conjecture can be written in logic notation as:

\forall n\in\mathbb{N},\left(\left(n\ge4\right)\wedge\left(n\, \mathrm{even}\right)\right)\Rightarrow\left(\exists p,q\in\mathbb{P},n=p+q\right)

A Goldbach number is a number that can be expressed as the sum of two odd primes. Therefore, another statement of Goldbach’s conjecture is that all even integers greater than 4 are Goldbach numbers.

The expression of a given even number as a sum of two primes is called a Goldbach partition of the number. For example:

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

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