Hassani, Mehdi and Majid, Narges Rezvani (2005) Primes in the Quadratic Intervals. Research report collection, 8 (1).

Abstract

In this note, we prove that for n ≥ 30, there exists at lest a prime number in the interval (n²,(n + f(n))²] in which f(n) is a function with the order of O(n/(ln²n)), and we count the number of primes in this interval. By using the result of this counting, we estimate the probability that a prime exists in the interval (n², (n + 1)²). Also, we show that there exists n₀ Є N such that for all n > n₀, the interval [(n − g(n))², n²), in which g(n) = O(n¹/²⁰).

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