Mathematics
which estimates the number of primes in the interval (x —y, x]. According to the Prime Number Theorem, the above estimate holds uniformly for cx^y^x, if c is any positive constant. Much work has been…
Primes of the Form [nc]Mathematics
Abstract A lower bound for πc(x), the number of primes of the form [nc] in [1, x], is given: πc(x) ⪢ x/log x. The significant point here is the longer range of c than formerly, namely 1 20 17 . The…
On the Distribution of ap Modulo OneMathematics
Abstract In this paper, we prove: "Suppose α is an irrational number and let || y || denote the smallest distance of y from an integer. Then, for any real number β, there are infinitely many primes p…
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