What is the answer to the Goldbach's conjecture

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In a letter in 1742 to his famous colleague, Leonhard Euler, the mathematician Christian Goldbach (1690-1764) suspected that that every even number> 2 is the sum of twoBe prime numbers. 4 = 2 + 2, 12 = 5 + 7, 28 = 5 + 23, 102 = 97 + 5 are such examples. To date, all of the examples reviewed have the Goldbach's conjecture confirmed, i.e. no even number> 2 has been found that cannot be represented as the sum of two prime numbers. A single counterexample would suffice, and Goldbach’s conjecture would be done once and for all. No matter how many correct examples there are, no mathematical proof can be replaced. Because of this, there is still no answer as to whether the guess is true or false.

If you reshape Goldbach’s hypothesis a little, you get the equivalent statement, that for every natural number n> 3 there are two prime numbers, so that n is equidistant from these two prime numbers.

Reason: Every even number can be written as twice a natural number, so 2n = p + q, where p, q are the two prime numbers. This is equivalent to n = (p + q) / 2, so that n is the mean of the two prime numbers. Applied to the number line, this means that n is the same distance from the two prime numbers p and q. Conversely, Goldbach's hypothesis follows from this claim: If there are two prime numbers p and q for every natural number n> 3, which are equidistant from n, then n = (p + q) / 2 and thus 2n = p + q, ie Goldbach's Hypothesis.

    With this equivalent statement, Goldbach’s hypothesis can easily be illustrated. The distances from zero to the left and right are entered on one of the number bars. On the second bar there is a number line from 0 to 99, with the prime numbers marked in red. You now put the “distance bar” over the bar with the number line, move the distance bar so that the zero comes to lie above the number n, whose prime partner p and q you are looking for. The answer can then be found quickly using the spacer bar.


    In this photo the number n = 27 was examined. The two prime numbers p = 23 and q = 31 are found at a distance of four units. Not only in this case there are other solutions, e.g. here the prime numbers 17 and 37. For Goldbach's conjecture, this means that the even number 54 (= 2 · 27) is the sum of the prime numbers 23 and 31 or 17 and 37 can be represented.

    It may be pointed out here that one is not a prime number. This regulation is related to the uniqueness of the prime factorization.

    It is actually unbelievable: There is a statement that is so easy to formulate that a child can understand it, for which only examples are known that confirm the claim, but there is no evidence far and wide in sight.

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