A091716 Standard deviation (rounded) of primes below 10^n.

2, 29, 298, 2962, 29412, 292821, 2921863, 29170821, 291324189, 2910238255, 29078387910, 290589147156, 2904276036695

Offset: 1

Author

Enoch Haga, Mar 05 2004

Keywords

• nonn
• more

Comments

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

Examples

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

References

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

Crossrefs

Cf. A092800, A092801, A092802.

Programs

Maple

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

Extensions

a(9)-a(13) from Hiroaki Yamanouchi, Sep 23 2014