An Elementary Proof of the Twin Prime Conjecture
Berndt Gensel
Abstract
Berndt Gensel
Abstract
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.
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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.
Key concepts: Twin prime, Mathematics, Coprime integers, Prime (order theory), Conjecture, Combinatorics, Generator (circuit theory), Discrete mathematics