Number Theory

    

Notes on the Proof of Second Hardy-Littlewood Conjecture

Authors: S. Roy

In this paper a slightly stronger version of the Second Hardy-Littlewood Conjecture, namely that inequality $\pi(x)+\pi(y) > \pi (x+y)$ s examined, where $\pi(x)$ denotes the number of primes not exceeding $x$. It is shown that the inequality holds for all sufficiently large x and y. It has also been shown that for a given value of $y \geq 55$ the inequality $\pi(x)+\pi(y) > \pi (x+y)$ holds for all sufficiently large $x$. Finally, in the concluding section an argument has been given to completely settle the conjecture.

Comments: 5 Pages.

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Submission history

[v1] 2014-10-13 04:16:43
[v2] 2014-10-13 07:49:37
[v3] 2014-10-18 07:04:05

Unique-IP document downloads: 763 times

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