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Goldbach Conjecture

Tool to check the Goldbach conjecture. The Goldbach conjecture proposes that any even integer number (greater than 2) can be written as the sum of two prime numbers.

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Goldbach Conjecture -

Tag(s) : Arithmetics

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Goldbach Conjecture

Goldbach Conjecture Calculator


Answers to Questions (FAQ)

What is Goldbach's conjecture?

The Goldbach conjecture is a still unproved proposition that any even integer (strictly greater than 2) can be written as the sum of 2 prime numbers.

Example: Decompositions in sum of 2 prime numbers: 4 = 2 + 2, 10 = 3 + 7 = 5 + 5, and so on.

Informatically, it is verified for all the even integers up to one billion of billion (and surely more advantage today because calculations are still in progress).

The program is limited to even integers less than 10^9 and also limited in number of decompositions.

What is the demonstration of the Goldbach's conjecture?

As the name suggests it is a conjecture, so to date it has no mathematical demonstration. Mathematicians suppose it to be true, and it is computer-verified up to very large numbers, but it does not prove that it is true for all numbers.

Why the number 2 is excluded?

The only way to decompose 2 into a sum (called list of partitions of 2) are: 1+1 and 0+2, as 0 and 1 are not prime numbers, it is not possible to verify Goldbach's conjecture for the number 2.

What is the verification algorithm of the Goldbach conjecture?

The algorithm is similar to that of a prime factors decomposition. It is possible to speed up the calculations by using an already calculated list of prime numbers.

// Javascript limited to n = 200
var pr = new Array(3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97);
function goldback(n) {
for (p in pr) {
if (pr[p] <= n/2 && in_array(n-pr[p], pr)) {
return n+=+pr[p]+++(n-pr[p]);
}
}
}

Source code

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