Notes on the Proof of Second Hardy-Littlewood Conjecture
نویسنده
چکیده
In this paper a slightly stronger version of the Second Hardy-Littlewood Conjecture (see [1]), namely that inequality π(x)+π(y) > π(x+y) is examined, where π(x) denotes the number of primes not exceeding x. It is shown that the inequality holds for all su ciently large x and y. It has also been shown that for a given value of y ≥ 55 the inequality π(x)+π(y) > π(x+y) holds for all su ciently large x. Finally, in the concluding section an argument has been given to completely settle the conjecture.
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تاریخ انتشار 2014