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Standard deviation (rounded) of primes below 10^n.
2

%I #11 Sep 23 2014 17:25:33

%S 2,29,298,2962,29412,292821,2921863,29170821,291324189,2910238255,

%T 29078387910,290589147156,2904276036695

%N Standard deviation (rounded) of primes below 10^n.

%C 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.

%C 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

%D John E. Freund, Modern elementary statistics, 5th ed. (Prentice-Hall, 1979), pp. 42-47

%e a(6) = 292821 (rounded from 292820.634) because this is the computed and rounded sample standard deviation of the 78498 primes below 10^6.

%p seq(round(Statistics:-StandardDeviation(select(isprime, [$2 .. 10^n-1]))),n=1..7); # _Robert Israel_, Sep 23 2014

%Y Cf. A092800, A092801, A092802.

%K nonn,more

%O 1,1

%A _Enoch Haga_, Mar 05 2004

%E a(9)-a(13) from _Hiroaki Yamanouchi_, Sep 23 2014