User:Neptunevn

1.0 Definition of Centromerick Numbers.
Any two numbers of natural row are called "chromosomick pair", if difference between them equals to a difference between their greatest prime factors. The number inside of this pair is called "centromerick".

''Example. The pair of numbers A=189 and B=195 is chromosomick, because 189=3*3*3*7 and 195=3*5*13. Difference (195 - 189) = (13 - 7)-difference between their greatest prime factors. From here we have 195 - 13 = 189 - 7 = 182, this number is Cm-number. Thus, the interval N[1 ...1000] contains 139 Cm-numbers: 6, 14, 15, 21, 33,, i.e. the interval N[100000. . . 100100] contains 17 Cm-numbers: 100007, 100013, 100015, 100021, 100033, 100036, 100039, 100073, 100081, 100082, 100083, 100084, 100087, 100091, 100097, 100098,100099.''

More formal algorithm for Cm-numbers calculations exist but these papers available only in Russian. Also, these documents include information about very unique properties of Cm-numbers logical relationships with biological DNA code, which might lead to further understanding and deciphering it.

2.0 How Centromerick Numbers properties relate to 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.

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 for 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. Category:Mathematical analysis