Re: Try to calculate

From: Tom St Denis (tomstdenis_at_iahu.ca)
Date: 05/30/03 

Date: Fri, 30 May 2003 03:27:21 GMT

????? wrote:
> 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.

I was approximating...

Tom

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