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A091716
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Standard deviation (rounded) of primes below 10^n.
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2
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2, 29, 298, 2962, 29412, 292821, 2921863, 29170821, 291324189, 2910238255, 29078387910, 290589147156, 2904276036695
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OFFSET
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1,1
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COMMENTS
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It appears that a good estimate for the standard deviation of primes below 10^(n+1) is about 10 times the term for 10^n.
Heuristically, if we use a model where each positive integer x has probability approximately 1/log(x) of being prime, we should expect the standard deviation of the primes below N to be approximately N/sqrt(12). - Robert Israel, Sep 23 2014
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REFERENCES
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John E. Freund, Modern elementary statistics, 5th ed. (Prentice-Hall, 1979), pp. 42-47
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LINKS
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EXAMPLE
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a(6) = 292821 (rounded from 292820.634) because this is the computed and rounded sample standard deviation of the 78498 primes below 10^6.
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MAPLE
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seq(round(Statistics:-StandardDeviation(select(isprime, [$2 .. 10^n-1]))), n=1..7); # Robert Israel, Sep 23 2014
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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