Re: Try to calculate

From: 小葉南洋杉 (john65537_at_yahoo.com.tw)
Date: 05/30/03 

Date: 29 May 2003 20:19:16 -0700

Tom St Denis <tomstdenis@iahu.ca> wrote in message news:<BYeBa.295811$w7k.235776@news04.bloor.is.net.cable.rogers.com>...
> ????? wrote:
> > I tried to calculate the number of primes of 512 bit long. Hope
> > someone may verify the result.
> > According to Gauss's prime number theorem, the number of primes less
> > than n should be n/ln(n).
> > 2^512/ln(2^512) - 2^511/ln(2^511) = ?
> > Using my PC's Calculator got 1.885305082130081660668523138413e+151,
> > Really big. Somthing you cannot store in any computer.
>
> Um? yea, you can't store 2^503 or so primes in memory, but yes you can
> store the number 2^503 in memory. For the record 2^503 ==
>
> 26187124863169134960105517574620793217733136368344518315866330944769\
> 07037123739643906616073860723325720709347302048056807373805236708314\
> 4426628220715008
>
> [Not particularly hard to calculate :-), you can do it by hand with
> about 8 squarings and 7 multiplications in under an hour or so].
>
> Tom

I'm not good at math, so I'd like to ask why the number of primes of
512 bits long is not 2^512/ln(2^512) - 2^511/ln(2^511) but 2^503?
Although they have the same order of 10's.

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