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 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.
متن کاملOn Small Intervals Containing Primes
Let p be an odd prime, such that pn < p/2 < pn+1, where pn is the n-th prime. We study the following question: with what probability does there exist a prime in the interval (p, 2pn+1)? After the strong definition of the probability with help of the Ramanujan primes ([11], [12])and the introducing pseudo-Ramanujan primes, we show, that if such probability P exists, then P ≥ 0.5. We also study a...
متن کاملPrimes in Beatty Sequences in Short Intervals
In this paper we show that sieve methods used previously to investigate primes in short intervals and corresponding Goldbach type problems can be modified to obtain results on primes in Beatty sequences in short intervals.
متن کاملPeriodicity in the Intervals between Primes
We consider the n(n−1)/2 uniquely defined positive intervals among the first n ≤ 10 prime numbers as a probe of the global nature of the sequence of primes. A statistically strong periodicity is identified in the counting function giving the total number of intervals of a certain size. The nature of the periodic signature implies that the sequences of intervals spanning fixed numbers of gaps re...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1974
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-25-4-375-391