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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Berndt Gensel (2020) studied this question.