Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved sieve of Eratosthenes   We show how to carry out a sieve of Eratosthenes up to N in space O(N^{1/3}
(log N)^{2/3}) and time O(N log N). These bounds constitute an improvement over
the usual versions of the sieve, which take space about O(sqrt{N}) and time at
least linear on N. We can also apply our sieve to any subinterval of [1,N] of
length Omega(N^{1/3} (log N)^{2/3}) in time essentially linear on the length of
the interval. Before, such a thing was possible only for subintervals of [1,N]
of length Omega(sqrt{N}).
  Just as in (Galway, 2000), our approach is related to Diophantine
approximation, and also has close ties to Voronoi's work on the Dirichlet
divisor problem. The advantage of the method here resides in the fact that,
because the method we will give is based on the sieve of Eratosthenes, we will
also be able to use it to factor integers, and not just to produce lists of
consecutive primes.

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The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
16
The categories of this paper are: stat
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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int