Monday, 28 May 2012

EQUAL NUMBERS OF INTERVALS


EQUAL NUMBERS OF INTERVALS. Any number N can be represented as the interval (0, N) consisting of a number of simple and composite numbers that are on the interval. N=(q+g)
(q) - the number of primes
(g) the number of composite numbers
(q+g) (=) (q/+g/) Equality of numbers at intervals, when (g=q/) the number of composite numbers on a smaller interval, equal to the number of Prime numbers in a large interval.
( = ) Sign of equality of numbers on intervals
Make a number of (P_n) - the number of primes such, when all of the numbers (g) (q) these numbers represent equity in intervals (g=q/).
For example, the beginning of number of number of number of number 11
(5+6)(=)(6+7)(=)(7+10)(=)(10+19)(=)(19+48)(=)(48+175)(=)(175+858)(=)(858+5801)(=)(5801+
11,,,,,,,,,13,,,,,,,,17,,,,,,,,,,,,29,,,,,,,,,,,,,,67,,,,,,,,,,,,,,223,,,,,,,,,,,,1033,,,,,,,,,,,,,6659,,,,,,,,,
By changing the beginning of the row, we will have a number of other, different from the first, from simple numbers. The beginning of the row, you should start from the simple number is not included in the already existing row, otherwise it will simply repeat the series with this number. For example, the beginning of 19
(8+11)(=)(11+20)(=)(20+51)(=)(71+282)(=)(282+1549)(=)(1549+11454)(=)(11454+
19,,,,,,,,,,,,,31,,,,,,,,,,,,,,71,,,,,,,,,,,,353,,,,,,,,,,,,,,1831,,,,,,,,,,,,,,13003,,,,,,,,,,,,,,,,,,,
And one more series for the example of the simple number 2
(2+0)(=)(0+3)(=)(3+2)(=)(2+3)(=)(3+2)
2,,,,,,,,,,,3,,,,,,,,,,,,,,5,,,,,,,,,,5,,,,,,,,,,,5
And one more series for the example of the simple number 7
(4+3)(=)(3+2)(=)(2+3)(=)(3+2)(=)(
Conclusion. When the number of primes greater than the number of composite numbers in the interval, a number of not growing. So did the right thing, for the beginning of the first series, with the number 11.

We will continue. Another series for example, a simple number 23
(9+14)(=)(14+29)(=)(29+80)(=)(80+329)(=)(329+1878)(=)(1878+
23,,,,,,,,,,,,,,,43,,,,,,,,,,,109,,,,,,,,,,,409,,,,,,,,,,,,,2207,,,,,,,,,,,,,
What we have, three infinite number of composed of some of primes, and the Prime numbers in the series are not repeated.
And such series
1) is Infinite?
2) until the Stop on the first question. Because a lot of questions.
3) How to find a Prime number (p_n) by its number (n)? Using the formula of the algorithm sieve of Eratosthenes.
4) the Addition to the first question. Why are some common number of the initial numbers of some, and not others, and what is their difference?
Sergey Sitnikov.

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