Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharpening "Primes is in P" for a large family of numbers   We give Deterministic Primality tests for large families of numbers. These
tests were inspired in the recent and celebrated Agrawal-Kayal-Saxena (AKS)
test. The AKS test has proved polynomial complexity O ((log n)^12) and they
expect it to be O ((log n)^6) . Our tests have proved complexity O ((log n)^6).
The complexity decreases to O ((log n)^4) as the power of 2 dividing n + 1 or n
- 1 increases. On large enough primes, our tests, in their worst case, run at
least 2^9 times faster than the AKS test.

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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc