Primes

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Pablo Yaggi

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Sep 26, 1998, 3:00:00 AM9/26/98
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Scott Nelson

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Sep 26, 1998, 3:00:00 AM9/26/98
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On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:

>Could anyone point me or give me a file with a list of primes up to the
>bigest known?
>Is there any like that? By the way wich is the bigest known?
>Pablo.
>

Do a web search on primes, and you'll turn up several web sites
with this info. Here's one such web site:
http://www.utm.edu/research/primes/largest.html
It has the list you asked for, though I suspect that when
you find out how big it is you'll want to refine your
search.

The largest primes found to date are Mersenne primes.
This one: 2^3021377-1 is largest known, and was found in 1998.
When written out in decimal, it's 909,526 digits.

----------------------------------------
DiehardC 1.03 now available via ftp from
ftp://helsbreth.org/pub/helsbret/random
Scott Nelson <sc...@helsbreth.org>

brin...@hotmail.com

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Sep 28, 1998, 3:00:00 AM9/28/98
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Hash: SHA1

In article <360CFF94...@cvtci.com.ar>,
Pablo Yaggi <pya...@cvtci.com.ar> wrote:
>
> Hi,


> Could anyone point me or give me a file with a list of primes up to
the
> bigest known?
> Is there any like that? By the way wich is the bigest known?
> Pablo.

So far there is no biggest known prime. Once a prime has been
discovered by some super computer, a new one is found not to long
after. It would be nice to know one of the highest prime numbers that
was discovered like yesterday or something. Believe me you don't a
list of all the primes. You definiately don't have the HD space and
neither do any of us here too.
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bo...@rsa.com

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Sep 28, 1998, 3:00:00 AM9/28/98
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In article <361024ab...@news.inreach.com>,

sc...@helsbreth.org wrote:
> On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:
>
> >Could anyone point me or give me a file with a list of primes up to the
> >bigest known?
> >Is there any like that? By the way wich is the bigest known?
> >Pablo.
> >
>
> Do a web search on primes, and you'll turn up several web sites
> with this info. Here's one such web site:
> http://www.utm.edu/research/primes/largest.html
> It has the list you asked for, though I suspect that when
> you find out how big it is you'll want to refine your
> search.
>
> The largest primes found to date are Mersenne primes.
> This one: 2^3021377-1 is largest known, and was found in 1998.
> When written out in decimal, it's 909,526 digits.

Which is why what the poster asked for is impossible. The poster asked for a
list of all primes up to the largest known. The universe isn't large enough
to hold such a list. Such a list would hold approximately 4.7 x 10^909519
primes. Put the radius of the universe at 5 Billion LY (~ 5 x 10^27 cm).
Assume one can list a prime in the volume of an atom (say 10^-24 cm^3). The
universe could hold about 10^107 primes. This is so far short of 10^909519
that it is hard to compare the two.

Further, it is faster to GENERATE a large list of primes than it is
to read it from disk or from the Net.

Further, one would never want to use such primes in a cryptographic
system.

Maybe the original poster can tell us what he REALLY wants?

Pablo Yaggi

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Sep 28, 1998, 3:00:00 AM9/28/98
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I'm the original poster, and what I want was a list of big primes, and I
got it from the point
from the first answer, so thank's a lot.
The prime list is for a friend who's working on prime generation, an old
guy who can't access the internet.
Thank's again,
Pablo.


Pablo Yaggi

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Sep 28, 1998, 3:00:00 AM9/28/98
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But (i forgot it),
I need to know the known primes, and the big list are just about the
Mersenne, and
the ones that are betwen?
So anybody has a list of primes that contains not only Mersenne but all?

Pablo


Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
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In article <6uo4tp$a2b$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
)In article <361024ab...@news.inreach.com>,
) sc...@helsbreth.org wrote:
)> On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:
)>
)> >Could anyone point me or give me a file with a list of primes up to the
)> >bigest known?
)> >Is there any like that? By the way wich is the bigest known?
)> >Pablo.
)> >
)>
)> Do a web search on primes, and you'll turn up several web sites
)> with this info. Here's one such web site:
)> http://www.utm.edu/research/primes/largest.html
)> It has the list you asked for, though I suspect that when
)> you find out how big it is you'll want to refine your
)> search.
)>
)> The largest primes found to date are Mersenne primes.
)> This one: 2^3021377-1 is largest known, and was found in 1998.
)> When written out in decimal, it's 909,526 digits.
)
)Which is why what the poster asked for is impossible. The poster asked for a
)list of all primes up to the largest known. The universe isn't large enough
)to hold such a list. Such a list would hold approximately 4.7 x 10^909519
)primes. Put the radius of the universe at 5 Billion LY (~ 5 x 10^27 cm).
)Assume one can list a prime in the volume of an atom (say 10^-24 cm^3). The
)universe could hold about 10^107 primes. This is so far short of 10^909519
)that it is hard to compare the two.

It is not impossible to list all known primes. We do not know 10^909519 primes
Where did you get this idea?

)
)Further, it is faster to GENERATE a large list of primes than it is
)to read it from disk or from the Net.
)
)Further, one would never want to use such primes in a cryptographic
)system.
)
)Maybe the original poster can tell us what he REALLY wants?
)
)-----== Posted via Deja News, The Leader in Internet Discussion ==-----
)http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum


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This message made from 100% recycled bits.
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Petr Konecny

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Sep 29, 1998, 3:00:00 AM9/29/98
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>>>>> Mike McCarty writes:

MM: In article <6uo4tp$a2b$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
MM: )In article <361024ab...@news.inreach.com>,
MM: ) sc...@helsbreth.org wrote:
MM: )> On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:
MM: )>
MM: )> >Could anyone point me or give me a file with a list of primes up to the
MM: )> >bigest known?
MM: )> >Is there any like that? By the way wich is the bigest known?
MM: )> >Pablo.
MM: )> >
MM: )>
MM: )> Do a web search on primes, and you'll turn up several web sites
MM: )> with this info. Here's one such web site:
MM: )> http://www.utm.edu/research/primes/largest.html
MM: )> It has the list you asked for, though I suspect that when
MM: )> you find out how big it is you'll want to refine your
MM: )> search.
MM: )>
MM: )> The largest primes found to date are Mersenne primes.
MM: )> This one: 2^3021377-1 is largest known, and was found in 1998.
MM: )> When written out in decimal, it's 909,526 digits.
MM: )
MM: )Which is why what the poster asked for is impossible. The poster asked for a
MM: )list of all primes up to the largest known. The universe isn't large enough
MM: )to hold such a list. Such a list would hold approximately 4.7 x 10^909519
MM: )primes. Put the radius of the universe at 5 Billion LY (~ 5 x 10^27 cm).
MM: )Assume one can list a prime in the volume of an atom (say 10^-24 cm^3). The
MM: )universe could hold about 10^107 primes. This is so far short of 10^909519
MM: )that it is hard to compare the two.

MM: It is not impossible to list all known primes. We do not know 10^909519 primes
MM: Where did you get this idea?

As seen above the original poster really asked for a file with list of
primes up to the largest known. The fact that we do not know all these
primes does not mean we are not able to estimate their number. The
computations make sense.

Petr Konecny <pekon at fi.muni.cz> http://www.fi.muni.cz/~pekon/

ke...@tgr.arg

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Sep 29, 1998, 3:00:00 AM9/29/98
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We do NOT know of 10^909519 primes!!! That number is only
approximately the SIZE of the largest known prime. So that number is
in fact the number of ALL integers up to that prime. Use the Prime
Number Thm applied to 10^909519 to get an approximate number of primes
up to that number.


Decrypt ke...@tgr.arg with ROT13 for my email addy.

Petr Konecny

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Sep 29, 1998, 3:00:00 AM9/29/98
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>>>>> keaak writes:

k: On Tue, 29 Sep 1998 02:22:02 GMT, Petr Konecny
k: <pekon+...@informatics.muni.cz> wrote:

::::::: Mike McCarty writes:
::
MM: In article <6uo4tp$a2b$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
MM: )In article <361024ab...@news.inreach.com>,
MM: ) sc...@helsbreth.org wrote:
MM: )> On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:
MM: )>
MM: )> >Could anyone point me or give me a file with a list of primes up to the
MM: )> >bigest known?
MM: )> >Is there any like that? By the way wich is the bigest known?
MM: )> >Pablo.
MM: )> >
MM: )>

MM: )> The largest primes found to date are Mersenne primes.
MM: )> This one: 2^3021377-1 is largest known, and was found in 1998.
MM: )> When written out in decimal, it's 909,526 digits.
MM: )

MM: )to hold such a list. Such a list would hold approximately 4.7 x 10^909519
::

MM: It is not impossible to list all known primes. We do not know 10^909519 primes
MM: Where did you get this idea?
::
:: As seen above the original poster really asked for a file with list of
:: primes up to the largest known. The fact that we do not know all these
:: primes does not mean we are not able to estimate their number. The
:: computations make sense.
::
:: Petr Konecny <pekon at fi.muni.cz> http://www.fi.muni.cz/~pekon/

::
::
::
k: We do NOT know of 10^909519 primes!!! That number is only
k: approximately the SIZE of the largest known prime. So that number is
k: in fact the number of ALL integers up to that prime. Use the Prime
k: Number Thm applied to 10^909519 to get an approximate number of primes
k: up to that number.

You mean that the number of primes less than n is
approximately n/ln(n) ?

Let n=2^3021377, then n/ln(n)=2^3021377/(3021377*ln(2)). To get the size
of this number we get log based 10 of it.

log (n/ln(n))=log (2^3021377/(3021377*ln(2)))=
3021377*log(2)-log(3021377) - log(ln(2))

My Pari/GP says that this is approximately:
909518.7841788726134905745563

So you are right we don't know of 10^909519 primes, but "only" about of
10^909518.78.

Douglas A. Gwyn

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Sep 29, 1998, 3:00:00 AM9/29/98
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Pablo Yaggi wrote:
> I need to know the known primes, and the big list are just about the
> Mersenne, and
> the ones that are betwen?
> So anybody has a list of primes that contains not only Mersenne but all?

There are *too many* primes to make a list of all primes
(up to some particular large prime).
When people need a large prime, they use a program
that *guesses* large numbers and tests them for
*probable* primality, until they find one that passes
the tests.

bo...@rsa.com

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Sep 29, 1998, 3:00:00 AM9/29/98
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In article <6upaok$192$1...@relay1.dsccc.com>,
jmcc...@sun1307.spd.dsccc.com (Mike McCarty) wrote:

> )> >Could anyone point me or give me a file with a list of primes up to the

> )> >bigest known?


> )> >Is there any like that? By the way wich is the bigest known?

> )> The largest primes found to date are Mersenne primes.


> )> This one: 2^3021377-1 is largest known, and was found in 1998.

> )> When written out in decimal, it's 909,526 digits.

> )


> )Which is why what the poster asked for is impossible. The poster asked for a

> )list of all primes up to the largest known. The universe isn't large enough

> )to hold such a list. Such a list would hold approximately 4.7 x 10^909519

> )primes. Put the radius of the universe at 5 Billion LY (~ 5 x 10^27 cm).

> )Assume one can list a prime in the volume of an atom (say 10^-24 cm^3). The

> )universe could hold about 10^107 primes. This is so far short of 10^909519

> )that it is hard to compare the two.
>

> It is not impossible to list all known primes. We do not know 10^909519 primes

> Where did you get this idea?

Bob gives yet another sigh of despair......

Doesn't anyone READ anymore? The poster asked (and I quote!)

"give me a file with a list of primes up to the bigest known?"

As was correctly observed, the largest known prime is M3021377. A list
of primes up to that number is impossible. Why is this so hard to understand?

And a list of ALL known primes is impossible. Suppose there were some
centralized list of primes. All of the KNOWN primes must also include
primes in people's PGP keys just to cite one example. There will always be
someone who knows some primes that are not on any given centralized list.
These primes are certainly "known". It would be impossible to gather all
known primes in a central list.

-----== Posted via Deja News, The Leader in Internet Discussion ==-----

bo...@rsa.com

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Sep 29, 1998, 3:00:00 AM9/29/98
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In article <36104171...@cvtci.com.ar>,
Pablo Yaggi <pya...@cvtci.com.ar> wrote:
> But (i forgot it),

> I need to know the known primes, and the big list are just about the
> Mersenne, and
> the ones that are betwen?
> So anybody has a list of primes that contains not only Mersenne but all?

I don't get it. I just don't.

I wrote out the arithmetic explaining why it was impossible for anyone to
have such a list. Are we speaking different languages or something?
Doesn't the word "impossible" convey meaning any more? Don't people read?

I must also state that the expression "the known primes" is not well-defined.
Known to whom? It is clear that no single list (even if such a thing could
exist) could hold all of the known primes because someone will "know" primes
that are not on that list!

Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
to
In article <qwwemsv...@decibel.fi.muni.cz>,
Petr Konecny <pekon+...@informatics.muni.cz> wrote:
)>>>>> Mike McCarty writes:
)
) MM: In article <6uo4tp$a2b$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
) MM: )In article <361024ab...@news.inreach.com>,
) MM: ) sc...@helsbreth.org wrote:
) MM: )> On Sat, 26 Sep 1998 Pablo Yaggi <pya...@cvtci.com.ar> wrote:
) MM: )>
) MM: )> >Could anyone point me or give me a file with a list of primes up to the
) MM: )> >bigest known?

The way I read this is:

Please tell me where I can get a list of all known primes.

I did not interpret it to mean a list of all primes, both known and
unknown (though I see it could be interpreted that way). And just
listing primes does not take much room, since the large ones we know can
be listed without giving their digits.

But the original poster will have to resolve this, I suppose.

[snip]

) MM: It is not impossible to list all known primes. We do not know 10^909519 primes
) MM: Where did you get this idea?
)
)As seen above the original poster really asked for a file with list of
)primes up to the largest known. The fact that we do not know all these
)primes does not mean we are not able to estimate their number. The
)computations make sense.
)
)Petr Konecny <pekon at fi.muni.cz> http://www.fi.muni.cz/~pekon/
)
)
)
)

Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
to
In article <6uqo6s$4us$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
)In article <36104171...@cvtci.com.ar>,
) Pablo Yaggi <pya...@cvtci.com.ar> wrote:
)> But (i forgot it),
)> I need to know the known primes, and the big list are just about the
)> Mersenne, and
)> the ones that are betwen?
)> So anybody has a list of primes that contains not only Mersenne but all?
)
)I don't get it. I just don't.
)
)I wrote out the arithmetic explaining why it was impossible for anyone to
)have such a list. Are we speaking different languages or something?
)Doesn't the word "impossible" convey meaning any more? Don't people read?

I think you are extremely obtuse and rude, especially when dealing with
someone whose native language is likely not English.

He wants a list of largest known primes across time.

)I must also state that the expression "the known primes" is not
well-defined.

I think you have a problem parsing English yourself.

)Known to whom? It is clear that no single list (even if such a thing could
)exist) could hold all of the known primes because someone will "know" primes
)that are not on that list!

Obtuse. In fact, I suspect deliberately so.

Mike

Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
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In article <6uqopk$5j5$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
)In article <6upaok$192$1...@relay1.dsccc.com>,

) jmcc...@sun1307.spd.dsccc.com (Mike McCarty) wrote:
)
)> )> >Could anyone point me or give me a file with a list of primes up to the
)> )> >bigest known?
)> )> >Is there any like that? By the way wich is the bigest known?
)
)> )> The largest primes found to date are Mersenne primes.
)> )> This one: 2^3021377-1 is largest known, and was found in 1998.
)> )> When written out in decimal, it's 909,526 digits.

)> )
)> )Which is why what the poster asked for is impossible. The poster asked for a
)> )list of all primes up to the largest known. The universe isn't large enough
)> )to hold such a list. Such a list would hold approximately 4.7 x 10^909519
)> )primes. Put the radius of the universe at 5 Billion LY (~ 5 x 10^27 cm).
)> )Assume one can list a prime in the volume of an atom (say 10^-24 cm^3). The
)> )universe could hold about 10^107 primes. This is so far short of 10^909519
)> )that it is hard to compare the two.
)>
)> It is not impossible to list all known primes. We do not know 10^909519 primes
)> Where did you get this idea?
)
)Bob gives yet another sigh of despair......
)
)Doesn't anyone READ anymore? The poster asked (and I quote!)
)
) "give me a file with a list of primes up to the bigest known?"

Yes. Certainly I did read it. I also did not interpret it to mean
a list of primes which are not known, especially since the word
"known" appeared specifically in the request.

You certainly are wound up tight.

Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
to
In article <36107B34...@null.net>,
Douglas A. Gwyn <DAG...@null.net> wrote:

)Pablo Yaggi wrote:
)> I need to know the known primes, and the big list are just about the
)> Mersenne, and
)> the ones that are betwen?
)> So anybody has a list of primes that contains not only Mersenne but all?
)
)There are *too many* primes to make a list of all primes
)(up to some particular large prime).

He asked for *known* primes, not *all* primes.

)When people need a large prime, they use a program
)that *guesses* large numbers and tests them for
)*probable* primality, until they find one that passes
)the tests.

Mike McCarty

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Sep 29, 1998, 3:00:00 AM9/29/98
to
In article <36104171...@cvtci.com.ar>,
Pablo Yaggi <pya...@cvtci.com.ar> wrote:
)But (i forgot it),
)I need to know the known primes, and the big list are just about the

)Mersenne, and
)the ones that are betwen?
)So anybody has a list of primes that contains not only Mersenne but all?
)
)Pablo

So I correctly interpreted the question after all.

Doesn't anyone READ, indeed.

Yes, there exists a prime homepage which will probably point you where
you need.

http://www.utm.edu/research/primes/

Mike

Scott Nelson

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Sep 29, 1998, 3:00:00 AM9/29/98
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On Tue, 29 Sep 1998 13:43:56 GMT, bo...@rsa.com wrote:

>
>I don't get it. I just don't.
>

>I wrote out the arithmetic explaining why it was impossible for anyone to

>have such a list. Are we speaking different languages or something?

>Doesn't the word "impossible" convey meaning any more? Don't people read?
>

There are several possibilities.

The poster might speak english so poorly he doesn't understand.
The poster might not understand math, or what a prime is.
The poster might be looking for something reasonable, but
has phrased it incorrectly.

But since this is Usenet, I think one should never discount
the possibility that poster is doing it intentionally, just
to piss you off.


Safuat Hamdy

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Sep 29, 1998, 3:00:00 AM9/29/98
to

jmcc...@sun1307.spd.dsccc.com (Mike McCarty) writes:
> )> So anybody has a list of primes that contains not only Mersenne but all?
> )

> )There are *too many* primes to make a list of all primes
> )(up to some particular large prime).
>
> He asked for *known* primes, not *all* primes.

Well, the original poster asked for a *list* of *all* primes (without
limitations). This is a fact, as you can see, period. It is correctly
observed that this is obviously not what he wants, unless he has really no
clue about primes. Now you interpret it to be all known primes, but then I
must repeat Bob's question: What the hell do you mean by *known* primes?
Known to whom?

--

S. Hamdy ha...@informatik.uni-hamburg.de
ha...@dpa.de

Unsolicited bulk or commercial email is not welcome.

Stanley Chow

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Sep 29, 1998, 3:00:00 AM9/29/98
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In article <6uqrj1$pkg$1...@relay1.dsccc.com>,

Mike McCarty <jmcc...@sun1307.spd.dsccc.com> wrote:
>)
>)I wrote out the arithmetic explaining why it was impossible for anyone to
>)have such a list. Are we speaking different languages or something?
>)Doesn't the word "impossible" convey meaning any more? Don't people read?
>
>I think you are extremely obtuse and rude, especially when dealing with
>someone whose native language is likely not English.

I don't know about that. You seem to have outdone Bob by a fair amount!
And to think - I used to complain about Bob's style! Bob must have mellowed
a bit.

>He wants a list of largest known primes across time.

That is not the original request. Bob correctly pointed out (with some
math that appears to be beyond many people) that the question as phrased
is not useful. It is not clear that the poster was having trouble with
english (at least it was not clear to me); it seemed to be a legitimate
expression of a poor question.

Your new interpretation of the question is clearly better phrased and
it is likely that someone will point to the FAQ site that has exactly
such a list (the URL escapes me and I don't have it bookmarked).


--
Stanle...@pobox.com (613) 763-6553
Me? Represent other people? Don't make them laugh so hard.

Roger Carbol

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Sep 29, 1998, 3:00:00 AM9/29/98
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Scott Nelson wrote:

> But since this is Usenet, I think one should never discount
> the possibility that poster is doing it intentionally, just
> to piss you off.


This is the most sensible advice I've seen for quite some time.

I think it especially applies to Usenet, but is not at all limited
to it.

.. Roger Carbol .. r...@shaw.wave.ca .. an early primer

bo...@rsa.com

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Sep 29, 1998, 3:00:00 AM9/29/98
to
In article <6uqr97$nbf$1...@relay1.dsccc.com>,

It did not say "list of known primes up to the biggest known" it said "list
of primes ...." There is a difference. I assume that if the poster meant
the former that he is intelligent enough to have said so.

>
> You certainly are wound up tight.

This is mathematics. I assume people mean what they ask. The original
question is not subject to "interpretation"; it is quite clear as to what is
being asked for. I assume people can write English. The assumption is
usually wrong, but to assume otherwise would be insulting to the person
asking the question.

So what happens?

I give a technical explanation for why what the poster wanted is impossible
and suddenly I am getting flamed etc.


After many years of frustration in *trying* to give honest answers to
questions and getting flamed for ones' responses you would be "wound up
tight" as well.

Don't you ever wonder why so few experts answer questions in this group?

Pablo Yaggi

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Sep 29, 1998, 3:00:00 AM9/29/98
to
Well, thank's a lot to everyone, and sorry for my first post, it was a
little confused (my English is not too good).
And finally I get the list with the bigest primes non-Mersenne.
So, is the best method for probing primarity the ECPP? for non-Mersenne,

anyone has the algorytm?
Pablo


mithen

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to
Safuat Hamdy wrote:
>
> jmcc...@sun1307.spd.dsccc.com (Mike McCarty) writes:
> > )> So anybody has a list of primes that contains not only Mersenne but all?
> > )
> > )There are *too many* primes to make a list of all primes
> > )(up to some particular large prime).
> >
> > He asked for *known* primes, not *all* primes.
>
> Well, the original poster asked for a *list* of *all* primes (without
> limitations). This is a fact, as you can see, period. It is correctly
> observed that this is obviously not what he wants, unless he has really no
> clue about primes.

This is not true.

The original message is (strait from dejanews)

:Hi,
:Could anyone point me or give me a file with a list of primes up to the
:bigest known?
:Is there any like that? By the way wich is the bigest known?
:Pablo.

'up to the biggest known' clearly indicates that there *is* a
restriction
and Mike's interpretation accurate.

Then the original poster made a second post (the one that you refered
to)
which occurs after the fact.

> Now you interpret it to be all known primes, but then I
> must repeat Bob's question: What the hell do you mean by *known* primes?
> Known to whom?

There isn't any room for interpretation, go read the original post and
thread.

-Pat Mucci

Joseph K. Nilaad

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to
Petr Konecny wrote:
>
>
> You mean that the number of primes less than n is
> approximately n/ln(n) ?
>
> Let n=2^3021377, then n/ln(n)=2^3021377/(3021377*ln(2)). To get the size
> of this number we get log based 10 of it.
>
> log (n/ln(n))=log (2^3021377/(3021377*ln(2)))=
> 3021377*log(2)-log(3021377) - log(ln(2))
>
How can you postulate equation above? Prime spacing is unpredictable!
Biggest known prime is 2^3021377-1, it doesn't mean that we have that
many primes.

Joe Nilaad
Nature is simple and beautiful...

Douglas A. Gwyn

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to
Mike McCarty wrote:
> The way I read this is:
> Please tell me where I can get a list of all known primes.

BobS was too polite to say so (up to this point),
so let me try:
That is a STUPID question!
No matter *how* you interpret it.

STL137

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

<<Prime spacing is unpredictable! >>
Um, duh?
Even I know that while prime spacing is unpredictable, it's pretty
well predictable how many primes there are under some N.
-----BEGIN PGP SIGNATURE-----
Version: PGPfreeware 5.5.5 for non-commercial use <http://www.nai.com>
Comment: Key ID 0xAC61CF7C

iQA/AwUBNhFu/XUitDysYc98EQISSwCfRAvrfFKQNpoSSAhVPt90qmzfQboAn2Fp
jr5f5m6KGgXOPa9i76UFNCO7
=vH5c
-----END PGP SIGNATURE-----

------
STL...@aol.com ===> Website: http://members.aol.com/stl137/
PGP keys: ~~~pgp.html Quotes: ~~~quotes.html
"I have sworn upon the altar of God eternal hostility against every form of
tyranny over the mind of man" - Thomas Jefferson


Dann Corbit

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to
APR-CL works well for numbers up to the hundreds of digits. You can get an
implementation of APR-CL with UBASIC. For thousands, I think you would want
to use ECPP. For special primes {such as Mersenne}, there are better ways
[obviously]. Both APR-CL and ECPP give a primality certificate. There may
be better ways, as I am not an expert by any stretch of the imagination.
--
Hypertext C-FAQ: http://www.eskimo.com/~scs/C-faq/top.html
C-FAQ ftp: ftp://rtfm.mit.edu, C-FAQ Book: ISBN 0-201-84519-9
Try "C Programming: A Modern Approach" ISBN 0-393-96945-2
Want Software? Algorithms? Pubs? http://www.infoseek.com

Pablo Yaggi wrote in message <36111B78...@cvtci.com.ar>...

Dann Corbit

unread,
Sep 29, 1998, 3:00:00 AM9/29/98
to
Douglas A. Gwyn wrote in message <36114263...@null.net>...
I don't know. I get a perverse joy looking at bazillions of digits of pi
and e. Maybe this guy is a prime freak. Perhaps he gets a strange and
wonderful joy looking at prime numbers and wanted the largest collection
currently possible. Maybe he is working on some sort of crypto system that
needs large primes. Who knows. I don't think the request is all that
unreasonable, but then, I think computing billions of digits of pi is a
great idea.

I think the problem with the request is that it is not clearly stated. If
he said:
"Is there a complete list of all primes between two and the largest known
Mersenne prime?" the answer would be "no."
If he said, "Is there a commonly used list of large primes?" the answer
would be "Yes, it is found at Chris Caldwell's prime page."

Are primes in the neighborhood of 2^64th known? I know I have calculated a
bunch of them. But I'll bet that there is not a complete list of them
anywhere. So the term "known primes" is indeed a problem. I think if math
and comp.sci newsgroups were mostly in French or Turkish I would have even
more difficulty communicating what I want to say than I do right now in
English.

I think the most logical step would be to ask for a clarification rather
than answering what we think it might possibly have meant.

Douglas A. Gwyn

unread,
Sep 30, 1998, 3:00:00 AM9/30/98
to
Pablo Yaggi wrote:
> Do you think all of us are STUPID, ...

Earth people are *all* stupid, stupid, stupid!

Douglas A. Gwyn

unread,
Sep 30, 1998, 3:00:00 AM9/30/98
to
Dann Corbit wrote:
> I think the problem with the request is that it is not clearly stated.

Yes, that is a more diplomatic way of putting it.
Not enough information was provided about the true purpose
to which the answer is to be put, to be able to answer effectively.
If somebody's attempted answer accidentally satisfied the need, fine.

bo...@rsa.com

unread,
Sep 30, 1998, 3:00:00 AM9/30/98
to
In article <36112F...@ssd.bna.boeing.com>,

"Joseph K. Nilaad" <jkni...@ssd.bna.boeing.com> wrote:
> Petr Konecny wrote:
> >
> >
> > You mean that the number of primes less than n is
> > approximately n/ln(n) ?
> >
> > Let n=2^3021377, then n/ln(n)=2^3021377/(3021377*ln(2)). To get the size
> > of this number we get log based 10 of it.
> >
> > log (n/ln(n))=log (2^3021377/(3021377*ln(2)))=
> > 3021377*log(2)-log(3021377) - log(ln(2))
> >
> How can you postulate equation above?

To which equation do you refer? What do you mean by 'postulate'?
The arithmetic is correct.

>Prime spacing is unpredictable!

True, but irrelevant.

The prime number theorem:

The number of primes less than x is approximately x/log x.

Alternatively, #primes < x = li(x) + O( exp(-3/5 sqrt(log x))) Where
li(x) is the logarithmic integral. The error term improves to O(x log x) if
one assumes RH.

> Biggest known prime is 2^3021377-1, it doesn't mean that we have that
> many primes.
>

This is gibberish. What does "have that many primes mean"? What does it
mean to "have" primes?

The entire set of primes up to M3021377 need not be known for us to
have a good estimate of its cardinality.

bo...@rsa.com

unread,
Sep 30, 1998, 3:00:00 AM9/30/98
to
In article <6us0or$8c3$1...@client3.news.psi.net>,

"Dann Corbit" <dco...@solutionsiq.com> wrote:
> APR-CL works well for numbers up to the hundreds of digits. You can get an
> implementation of APR-CL with UBASIC. For thousands, I think you would want
> to use ECPP. For special primes {such as Mersenne}, there are better ways
> [obviously]. Both APR-CL and ECPP give a primality certificate. There may
> be better ways, as I am not an expert by any stretch of the imagination.
>

If you are not an expert, why do you insist on spouting misinformation??

(1) APR-CL is uniformly faster than ECPP up to current computational
limits. (several thousand decimal degits). It is the fastest current method.

(2) APR-CL does NOT, repeat NOT produce a certificate. That is its major
problem (apart from difficulty of implementation). ECPP does produce one.

Stephen M. Gardner

unread,
Sep 30, 1998, 3:00:00 AM9/30/98
to
bo...@rsa.com wrote:
> Doesn't the word "impossible" convey meaning any more? Don't people read?

Okay, I give up. How much written evidence of people not reading
simple declarative English sentences does it take to convince you that
people can't read? You seem reluctant to grasp this rather simple fact
about human nature. Can't *you* read? ;-) The evidence is right there in
black and white. ;-) ;-) ;-) ;-) ;-) ;-) ;-) ;-)

Seriously, this is really not worth a brain aneurysm. People don't
read. I happens to all of us. And what's more, most people really can't
grasp the cardinality of the set of integers, let alone how many of
these strange things called primes there are. Here's the kicker though.
It is equally difficult for the mathematically trained to grasp just how
unequally distributed their knowledge is. In fact, I think I would say
that it is far more difficult for mathematicians to truly grasp how rare
their knowledge is in the human population than it is for a
non-mathematician to grasp how many primes there are between 3 and the
millionth Mersenne prime.

> I must also state that the expression "the known primes" is not well-defined.

> Known to whom? It is clear that no single list (even if such a thing could

> exist) could hold all of the known primes because someone will "know" primes

> that are not on that list!

You know a great deal about the distribution of primes among the
integers. You seem however, less well informed about the distribution of
mathematical knowledge in the human population. You should probably get
out more. Perhaps if you went to a shopping mall in a suit with a
clipboard and asked some well chosen questions about about prime number
facts . . . You might gain some insight before mall security came and
led you off screaming: "But you don't understand! We can't know all the
primes! Can't you people read?! They are as unknowable as the mind of
GOOOOODDD!" A couple of days in a nice dark quiet room with nice drugs
and gentle nurses and you will be right as rain. ;-)

When I was young and foolish it used to outrage me that so many people
seemed so ignorant, even stupid. Then I got old and wise and realized
that that was a good thing for the old and wise. Yes Pangloss, we must
consider this a feature, not a bug, in this best of all possible worlds.

--
Take a walk on the wild side: http://www.metronet.com/~gardner/
Still a lot of lands to see but I wouldn't want to stay here,
it's too old and cold and settled in its ways here.
Joni Mitchell ("California")

Andrew John Walker

unread,
Oct 1, 1998, 3:00:00 AM10/1/98
to
bo...@rsa.com writes:

>In article <6us0or$8c3$1...@client3.news.psi.net>,
> "Dann Corbit" <dco...@solutionsiq.com> wrote:
>> APR-CL works well for numbers up to the hundreds of digits. You can get an
>> implementation of APR-CL with UBASIC. For thousands, I think you would want
>> to use ECPP. For special primes {such as Mersenne}, there are better ways
>> [obviously]. Both APR-CL and ECPP give a primality certificate. There may
>> be better ways, as I am not an expert by any stretch of the imagination.
>>

>If you are not an expert, why do you insist on spouting misinformation??

>(1) APR-CL is uniformly faster than ECPP up to current computational
>limits. (several thousand decimal degits). It is the fastest current method.

>(2) APR-CL does NOT, repeat NOT produce a certificate. That is its major
>problem (apart from difficulty of implementation). ECPP does produce one.

Does anyone have pointers to implementations of these, preferably
MSDOS? I have the UBASIC package, but it must be possible to go faster!
--
* Andrew Walker *
* Department Of Physics * e-mail -- aj...@uow.edu.au
* Wollongong University *
* Australia *

Robert G. Durnal

unread,
Oct 1, 1998, 3:00:00 AM10/1/98
to
In <360FEB99...@cvtci.com.ar>, Pablo Yaggi <pya...@cvtci.com.ar> wrote:
: I'm the original poster, and what I want was a list of big primes, and I
: got it from the point
: from the first answer, so thank's a lot.
: The prime list is for a friend who's working on prime generation, an old
: guy who can't access the internet.
: Thank's again,
: Pablo.

I don't know what prime lengths you are interested in, but I recently
wrote a 32-bit DOS version of the Miller-Rabin prime test, generating a list
of 32-bit strong primes. Theory says that there are about 93,000,000 primes
between 2^31 and 2^32; in a few hours I found 1,530,000 strong primes (where
(p-1)/2 is also prime) and have these posted on http://members.tripod.com/
~afn21533/ with file names PRIMES01 to PRIMES09. Each file is ZIPped, and
contains 9 subfiles with 20,000 primes each. Feel free to use them for whatever
purpose you wish, and if you are interested in the source for the M-R
program, contact me.
----------------
My home page URL=http://members.tripod.com/~afn21533/ Robert G. Durnal
Hosting HIDE4PGP, HIDESEEK v5.0, PGE, TinyIdea (link) afn2...@afn.org
and BLOWFISH in both Windows and mini-DOS versions. afn2...@my-dejanews.com
ITAR may apply, so look for instructions.

Dann Corbit

unread,
Oct 1, 1998, 3:00:00 AM10/1/98
to
bo...@rsa.com wrote in message <6utevm$fhd$1...@nnrp1.dejanews.com>...

>In article <6us0or$8c3$1...@client3.news.psi.net>,
> "Dann Corbit" <dco...@solutionsiq.com> wrote:
>> APR-CL works well for numbers up to the hundreds of digits. You can get
an
>> implementation of APR-CL with UBASIC. For thousands, I think you would
want
>> to use ECPP. For special primes {such as Mersenne}, there are better
ways
>> [obviously]. Both APR-CL and ECPP give a primality certificate. There
may
>> be better ways, as I am not an expert by any stretch of the imagination.
>>
>
>If you are not an expert, why do you insist on spouting misinformation??
>
>(1) APR-CL is uniformly faster than ECPP up to current computational
>limits. (several thousand decimal degits). It is the fastest current
method.


I was quoting some idiot from a previous message in this group. No doubt he
did not have any idea what he was talking about. You're right, I really
should look carefully at where I get my information.

From a previous thread:
"> Can you prove that a
> 1000 digit number which may be a prime or a Charmichael number is prime or
> not in a reasonable period of time?
In a word, yes. I would call just a few days on a single workstation
reasonable. ECPP can do it in about 2-3 days. APR-CLB can do it in about
1/2 that time. (However for larger numbers ECPP becomes faster)"

Jim Schaerer

unread,
Oct 1, 1998, 3:00:00 AM10/1/98
to
On Tue, 29 Sep 1998 13:53:56 GMT, bo...@rsa.com wrote this to the
following group(s) - sci.crypt:

>[A] list of ALL known primes is impossible. Suppose there were some
>centralized list of primes. All of the KNOWN primes must also include
>primes in people's PGP keys...

Ok. This is the point I don't understand. I thought that PGP keys
were created based on probable primes. (i.e., 99.99999999999% chance
of being prime), and not true primes. If one could prove a PGP key
prime (which would mean factoring it, correct?), then there would be
no point in using PGP.

Again, this is something I don't understand. I am not trying to
correct anyone. I'm sure my misunderstanding is due to my own
ignorance of the subject matter. I simply seek understanding and
enlightenment ;-).

Thanks!


- Jim Schaerer
------------------------------------
To respond via e-mail, remove the
obvious "NOSPAM" from my address
(NOSPA...@swbell.net).

Stephen M. Gardner

unread,
Oct 1, 1998, 3:00:00 AM10/1/98
to
bo...@rsa.com wrote:
> If you are not an expert, why do you insist on spouting misinformation??
That's right boys and girls. Only experts are allowed to spout
misinformation. You tell 'em bob. Damned neophytes trying to take the
bread out of the mouthes of the experts. ;-)

Douglas A. Gwyn

unread,
Oct 2, 1998, 3:00:00 AM10/2/98
to
Stephen M. Gardner wrote:
> bo...@rsa.com wrote:
> > If you are not an expert, why do you insist on spouting misinformation??
> That's right boys and girls. Only experts are allowed to spout
> misinformation. You tell 'em bob. Damned neophytes trying to take the
> bread out of the mouthes of the experts. ;-)

Yeah, why be misinformed by others, when you can come to us?

bo...@rsa.com

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Oct 2, 1998, 3:00:00 AM10/2/98
to
In article <6uvvhh$csb$1...@maya.ece.ufl.edu>,

afn2...@freenet2.afn.org (Robert G. Durnal) wrote:
> In <360FEB99...@cvtci.com.ar>, Pablo Yaggi <pya...@cvtci.com.ar> wrote:
> : I'm the original poster, and what I want was a list of big primes, and I
> : got it from the point
> : from the first answer, so thank's a lot.
> : The prime list is for a friend who's working on prime generation, an old
> : guy who can't access the internet.

> I don't know what prime lengths you are interested in, but I recently


> wrote a 32-bit DOS version of the Miller-Rabin prime test, generating a list
> of 32-bit strong primes. Theory says that there are about 93,000,000 primes
> between 2^31 and 2^32; in a few hours I found 1,530,000 strong primes


Allow me to point out that it should should only have taken at worst a few
minutes, rather than hours to generate such a list. Use a sieve next time,
rather than Miller-Rabin. Furthermore, you don't even need Miller-Rabin as
all base 2,3,5,7 ordinary pseudoprimes have been identified up to 25 x 10^9.

Using the right algorithm is most of the battle. Too bad people always plunge
ahead with computing before studying the literature to see what has already
been done.


>(where
> (p-1)/2 is also prime) and have these posted on http://members.tripod.com/
> ~afn21533/ with file names PRIMES01 to PRIMES09. Each file is ZIPped,

A waste of disk space. It is faster to generate them, then read them over
the net.


Bob's Basic Maxim:

The sooner you start computing, the longer it will take to finish.

-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own

bo...@rsa.com

unread,
Oct 2, 1998, 3:00:00 AM10/2/98
to
In article <3614ef27....@1.0.0.2>,

NOSPA...@swbell.net (Jim Schaerer) wrote:
> On Tue, 29 Sep 1998 13:53:56 GMT, bo...@rsa.com wrote this to the
> following group(s) - sci.crypt:
>
> >[A] list of ALL known primes is impossible. Suppose there were some
> >centralized list of primes. All of the KNOWN primes must also include
> >primes in people's PGP keys...
>
> Ok. This is the point I don't understand. I thought that PGP keys
> were created based on probable primes. (i.e., 99.99999999999% chance
> of being prime), and not true primes. If one could prove a PGP key
> prime (which would mean factoring it, correct?)

A PGP public key is composite not prime. And one does not prove a number
prime by trying to factor it.

>, then there would be
> no point in using PGP.

A number is either prime of it isn't. The probability that a number is prime
is either 1 or 0. Period. One can test a candidate number with a decision
procedure and the decision procedure can have a probability of error.
But that is NOT the same as saying the number has a (certain) probability
of being prime.

Furthermore, it is NOT required that the keys be generated by numbers which
have passed a probabilistic test. One can still use a deterministic method
to determine the primes.


Also, PGP keys are not prime. They are the product of two primes. The two
primes constitute a *secret* key. This key is not revealed. Thus, you
know two primes that noone else does.......


I routinely generate primes in my work. I am sure that among them are primes
that have never appeared on any central list. Trying to gather a centralized
list of all *known* primes is impossible.

bo...@rsa.com

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Oct 2, 1998, 3:00:00 AM10/2/98
to
In article <361426B7...@metronet.com>,

"Stephen M. Gardner" <gar...@metronet.com> wrote:
> bo...@rsa.com wrote:
> > If you are not an expert, why do you insist on spouting misinformation??
> That's right boys and girls. Only experts are allowed to spout
> misinformation. You tell 'em bob. Damned neophytes trying to take the
> bread out of the mouthes of the experts. ;-)

You really don't get it do you?? Yes, I read the smiley.

I have to spend too much of my time correcting misinformation heard by
clients (and others). Most of the time it is "something they heard on the
Internet".

DON'T REPEAT RUMORS.

Don't repeat "something you heard" without checking it.

Don't give answers to technical questions unless you have studied the subject
and are sure of your facts.

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