1Berndt Gensel, Carinthia University of Applied Sciences, Austria
Turkish Journal of Analysis and Number Theory.
2020,
Vol. 8 No. 3, 52-56
DOI: 10.12691/tjant-8-3-1
Copyright © 2020 Science and Education PublishingCite this paper: B. Gensel. An Elementary Proof of the Twin Prime Conjecture.
Turkish Journal of Analysis and Number Theory. 2020; 8(3):52-56. doi: 10.12691/tjant-8-3-1.
Correspondence to: B. Gensel, Berndt Gensel, Carinthia University of Applied Sciences, Austria. Email:
b.gensel@fh-kaernten.atAbstract
It is well known that every prime number
has the form
or
We will call
the
generator of
Twin primes are distinghuished due to a
common generator for each pair. Therefore it makes sense to search for the Twin Primes on the level of their generators. This paper present a new approach to prove the
Twin Prime Conjecture by a sieve method to extract all Twin Primes on the level of the Twin Prime Generators. We define the
--numbers
as numbers for which holds that
and
are coprime to the prime
By dint of the average distance
between the
--numbers we can prove the
Twin Prime Conjecture indirectly.
Keywords