Re: Try to calculate

From: 小葉南洋杉 (john65537_at_yahoo.com.tw)
Date: 05/31/03 

Date: 30 May 2003 19:28:49 -0700

Tom St Denis <tomstdenis@iahu.ca> wrote in message news:<tcABa.307087$w7k.303132@news04.bloor.is.net.cable.rogers.com>...
> ????? wrote:
> > Tom St Denis <tomstdenis@iahu.ca> wrote in message news:<BYeBa.295811$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

Funny, Gauss's prime number theorem is also an approximation.

Relevant Pages

  • Re: Chez Watt: Prime Idiocy
    ... I can now understand why you haven't attempted any math in support of your ... There is a disclaimer that the lists are only ... listing of the first seven primes, then it is hardly irrelevant to point ... to mathematical skill. ...
    (talk.origins)
  • Re: JSH: Thats why insults are used
    ... non-polynomial factorization--enough for a math journal to just keel ... So, the twin primes conjecture is a probability question, as is ... The insults used against me, the webpages, and all the hostile behavior ... I've yet to see one post from you without any social crap. ...
    (sci.math)
  • Re: JSH: Thats why insults are used
    ... non-polynomial factorization--enough for a math journal to just keel ... So, the twin primes conjecture is a probability question, as is ... political behavior, as I've noted, but why do people resort to ... The insults used against me, the webpages, and all the hostile behavior ...
    (sci.math)
  • JSH: Thats why insults are used
    ... It's harder and harder to see how mathematicians missed such simple ... non-polynomial factorization--enough for a math journal to just keel ... So, the twin primes conjecture is a probability question, as is ... The insults used against me, the webpages, and all the hostile behavior ...
    (sci.math)
  • Re: fooling primality tests
    ... Tom St Denis wrote: ... are needed "only" the primes from 2 to ... [goto the zetagrid ...
    (sci.crypt)