Submitted:
14 November 2022
Posted:
15 November 2022
Read the latest preprint version here
Abstract
We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.
Keywords:
Sieve of Eratosthenes
; Goldbach conjecture
; Polignac conjecture
; Twin Prime conjecture
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