منابع مشابه
Primes in Short Intervals
Contrary to what would be predicted on the basis of Cramér’s model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x + H) − ψ(x), for 0 ≤ x ≤ N , is approximately normal with mean ∼ H and variance ∼ H logN/H , when N ≤ H ≤ N1−δ .
متن کاملA note on primes in short intervals
This paper is concerned with the number of primes in short intervals. We present a method to use mean value estimates for the number of primes in (x, x+x] to obtain the asymptotic behavior of ψ(x+x)−ψ(x). The main idea is to use the properties of the exceptional set for the distribution of primes in short intervals. Mathematics Subject Classification (2000). 11NO5.
متن کاملA note on Primes in Short Intervals
Instead of a strong quantitative form of the Hardy-Littlewood prime k-tuple conjecture, one can assume an average form of it and still obtains the same distribution result on ψ(x + h) − ψ(x) by Montgomery and Soundararajan [1].
متن کاملLonger than Average Intervals Containing No Primes
We present two methods for proving that there is a positive proportion of intervals which contain no primes and are longer than the average distance between consecutive primes. The first method is based on an argument of Erdös which uses a sieve upper bound for prime twins to bound the density function for gaps between primes. The second method uses known results about the first three moments f...
متن کاملSums of Primes and Squares of Primes in Short Intervals
Let H2 denote the set of even integers n 6≡ 1 (mod 3). We prove that when H ≥ X, almost all integers n ∈ H2 ∩ (X,X + H] can be represented as the sum of a prime and the square of a prime. We also prove a similar result for sums of three squares of primes.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1982
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-42-1-91-96