- 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 at earthlink.net

miltbrown@...

[Non-text portions of this message have been removed] - Milton Brown wrote:
> The number of primes with exactly 100

No. Using the approximation pi(n) = n/ln n, the number of 200-digit primes is

> digits is approximately 4*10^97. The

> number of primes with exactly 200 digits

> is approximately 2.4*10^196.

around 2*10^197.

> Does this mean that density of 200 digit

No. The approximate ratio is 0.5.

> primes is approximately

>

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

>

> primes?

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