Authors: Ricardo G. Barca
The binary Goldbach conjecture asserts that every even integer greater than 4 is the sum of two primes. In order to prove this statement, we start by defining a kind of double sieve of Eratosthenes as follows. Given an even integer x, we sift out from [1, x] all those elements that are congruents to 0 modulo p, or congruents to x modulo p, where p is a prime less than the square root of x. So, any integer in the interval [sqrt{x}, x] that remains unsifted is a prime p for which either x-p = 1 or x-p is also a prime. Then, we introduce a new way to formulate this sieve, which we call the sequence of k-tuples of remainders. Using this tool, we obtain a lower bound for the number of elements in [1, x] that survives the sifting process. We prove, for every even number x greater than the square of 149, that there exist at least 3 integers in the interval [ 1, x ] that remains unsifted. This proves the binary Goldbach conjecture for every even number x greater than the square of 149, which is our main result.
Comments: 43 Pages. Extended explanation in the Introduction.
Download: PDF
[v1] 2012-03-17 12:38:17 (removed)
[v2] 2012-04-05 08:25:08 (removed)
[v3] 2017-06-04 07:54:04
[v4] 2017-09-10 09:26:00
Unique-IP document downloads: 398 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.