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Centromerick numbers and Goldbach’s conjecture.

The numbers X and Y make up a chromosome pair, if difference between them Y – X is equal to difference between their greatest prime factors Py – Px. From here we have: Y – X = Py – Px, or Y – Py = X – Px. The last number is called by “centromerick” (CM-number). For example, if Y = 68, X = 54, Py = 17, and Px=3; CM-number = 51. The name "cetromerick" is a unique word which derived from the fact that these numbers resembles DNA Centromere structure.

According to this definition we have a sequence of CM-numbers: 6, 14, 15, 21, 33, 35, 45, 51, 55, 62, 69, 77, 78, 85, 91, 93, 95, 116, 119, 130, 133, 141, 143, 145, 155, 159, 161, 182, 187, 189, 195, 203, etc. There is more detailed information in the papers but it is available only in Russian. Mathematicians know very well about the problem of X. Goldbach (1690 – 1764). For multitude of prime numbers it means: “every prime number, greater than 3, can be written as a sum of at most three primes”. Professor V.N.Brandin offer a new and unique hypotheses with an analogous conjecture for the multitude of CM-numbers: “every CM-number, starting with 21, can be written as a sum of at most three CM-numbers”.

For example: 21 = 6+15, 33 = 6+6+21,…, 51 = 6+45,…, 78 = 6+21+51,…,483 = 21+33+429, etc. It has been shown by him fpr only 500 numbers, that this conjecture is right for all CM-numbers. The problem is that such conjectures can’t be proven throw calculation. Although appeared to be a bit mysterious, but this unique hypothesis arises precisely here.

Multitudes of prime numbers and CM-numbers don’t have intersection. CM-numbers are more complex than prime numbers. They are both, odd and even, and can be just in contact. Why such different objects have almost the same problems? Perhaps, they have something common on a generic level, and then we must investigate two conjectures together.