Authors: Alexander Fedorov
One of causes why Twin Primes problem was unsolved over a long period is that pairs of Twin Primes (PTP) are considered separately from other pairs of Twin Numbers (PTN). By purpose of this work is research of connections between different types of PTN. For realization of this purpose by author was developed the "Arithmetic of pairs of Twin Numbers" (APTN). In APTN are defined three types PTN. As shown in APTN all types PTN are connected with each other by relations which represent distribution of prime and composite positive integers less than n between them. On the basis of this relations (axioms APTN) are deduced formulas for computation of the number of PTN (NPTN) for each types. In APTN also is defined and computed Average value of the number of pairs are formed from odd prime and composite positive integers $ < n $ . Separately AVNPP for prime and AVNPC for composite positive integers. We also deduced formulas for computation of deviation NPTN from AVNPP and AVNPC. It was shown that if $n$ go to infinity then NPTN go to AVNPC or AVNPP respectively that permit to apply formulas for AVNPP and AVNPC to computation of NPTN. At the end is produced the proof of the Twin Primes problem with help of APTN. It is shown that if n go to infinity then NPTP go to infinity.
Comments: 25 Pages.
Unique-IP document downloads: 173 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.