• The number of primes with exactly 100 digits is approximately 4*10^97.The number of primes with exactly 200 digits is approximately 2.4*10^196. Does this mean
Message 1 of 2 , Jun 13, 2004
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The number of primes with exactly 100
digits is approximately 4*10^97.The
number of primes with exactly 200 digits
is approximately 2.4*10^196.

Does this mean that density of 200 digit
primes is approximately

1/17 = 2.4/40 less dense than 100 digit

primes?

Milton L. Brown
miltbrown@...

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• ... No. Using the approximation pi(n) = n/ln n, the number of 200-digit primes is around 2*10^197. ... No. The approximate ratio is 0.5. The density of primes
Message 2 of 2 , Jun 14, 2004
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Milton Brown wrote:
> The number of primes with exactly 100
> digits is approximately 4*10^97. The
> number of primes with exactly 200 digits
> is approximately 2.4*10^196.

No. Using the approximation pi(n) = n/ln n, the number of 200-digit primes is
around 2*10^197.

> Does this mean that density of 200 digit
> primes is approximately
>
> 1/17 = 2.4/40 less dense than 100 digit
>
> primes?

No. The approximate ratio is 0.5.
The density of primes is around reversely proportional to the number of digits,
i.e. twice the digits, half the chance.
A simple approximation to the density near n is 1/ln n.

--
Jens Kruse Andersen
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