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• ... To quote from the definitive web resource on prime numbers: http://www.utm.edu/research/primes/notes/faq/LongestList.html The problem with answering this
Message 1 of 8 , Mar 5, 2001
> There are IN FACT bulk sequences of primes up to 19 digits in length
> at the MegaNumberS web site.

To quote from the definitive web resource on prime numbers:

http://www.utm.edu/research/primes/notes/faq/LongestList.html

"The problem with answering this question is small primes are too
easy to find. The can be found far faster than they can be read from
a hard disk, so no one bothers to keep long lists (say past 10^9).
Long lists just waste storage, and on the Internet, they just waste
bandwidth."

This quote applies whether you're talking about 15 digit primes or
19 digit primes (yes, 19 digit primes are small); in either case, any
decent prime generation program will generate these numbers faster than
you can ship them across the network.

Also, if Chris Harrison has any intention of these lists of primes
ever being used for any real purpose, a few suggestions:

(1) Be consistent in your data format. You have plain text files,
StuffIt files, and ZIP files -- the one ZIP file I downloaded
had an RTF text file inside. Nobody is going to write an RTF
parser to pull ASCII numbers from a data file.

Use a binary encoding; you'll get better (much better)
compression than any generalized compressor like ZIP or StuffIt.
Make it a simple one, such as encoding the gaps between primes
into individual bytes. Document the format and provide source
code for a sample decoder.

(2) Go much bigger than 19 digit primes -- start with 100 digit
primes.

(3) The best option of all -- provide the program which generates
• ... My mail receiving operation M could be nilpotent. Or maybe M is idempotent. Perhaps neither of the above. If so, and M^2 == I... ... You should see my
Message 2 of 8 , Mar 5, 2001
On Mon, 05 March 2001, Chris Harrison wrote:
> Dear All,
>
> Please be aware that I have e-mailed Phil Carmody TWICE to ask him to
> correct his assertion copied below:

My mail receiving operation M could be nilpotent.
Or maybe M is idempotent.
Perhaps neither of the above. If so, and M^2 == I...

> >On Sun, 04 March 2001, "�� ����" wrote:
> > who can give me a twin primes table below 1024 bits,or an address, thank you!
>
> >on't be fooled by the name, these only go up to 15 digits:
> >http://www.meganumbers.com/
>
> >If you want anything larger, your best bet is to generate them yourself.
>
> and he has not responded, hence this e-mail.

You should see my inbox! One tediously long meeting and lunch - that's all it takes.
At least we know the primenumbers list is "active" now!

> There are IN FACT bulk sequences of primes up to 19 digits in length
> at the MegaNumberS web site.

My mistake, sorry. However, as has been noted elsewhere, 10^19 is still "small" compared to the ~1000 bit range being mentioned. I'd not actually perused the 'meganumbers' site before, so wasn't previously aware of what it contained. However, as this side of the globe was awake, and the Americans were probably asleep, I thought that I'd do the "run around the primepages finding pointers" job. It's only those that actually do things that get criticised, so I don't feel too bad at having one bogus character in my entire reply.

Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
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• At 11:45 AM 3/5/2001 +0000, Chris Harrison wrote: There are IN FACT bulk sequences of primes up to 19 digits in length ... I ve got a list up to 2^32, which is
Message 3 of 8 , Mar 5, 2001
At 11:45 AM 3/5/2001 +0000, Chris Harrison wrote:
There are IN FACT bulk sequences of primes up to 19 digits in length
>at the MegaNumberS web site.

I've got a list up to 2^32, which is about 19 digits, but that is a long
way from the requested 2^1024.

+--------------------------------------------------------+
| Jud McCranie |
| |
| 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
+--------------------------------------------------------+
• ... I keep my list up to 2^32 on disk, even though I think it would be faster to generate them. (At some point it becomes slower to generate them.) The
Message 4 of 8 , Mar 5, 2001
At 07:47 AM 3/5/2001 -0500, Jack Brennen wrote:

> "The problem with answering this question is small primes are too
> easy to find. The can be found far faster than they can be read from
> a hard disk, so no one bothers to keep long lists (say past 10^9).
> Long lists just waste storage, and on the Internet, they just waste
> bandwidth."

I keep my list up to 2^32 on disk, even though I think it would be faster
to generate them. (At some point it becomes slower to generate them.) The
reason I do that rather than generate them each time is for
reliability. If I'm looking at primes of a certain type, I read them in
and check. I think this is saver than changing the generating program each
time. Also the program to read them in is a lot shorter and less prone to
error than the generating program.

+--------------------------------------------------------+
| Jud McCranie |
| |
| 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
+--------------------------------------------------------+
• ... I ve got something similar on my website - a short description of primes, with C source to programs to generate and read primes in a successive-differences
Message 5 of 8 , Mar 5, 2001
At 11:50 AM 3/5/01 -0500, Jud McCranie wrote:
>At 07:47 AM 3/5/2001 -0500, Jack Brennen wrote:
>
>> "The problem with answering this question is small primes are too
>> easy to find. The can be found far faster than they can be read from
>> a hard disk, so no one bothers to keep long lists (say past 10^9).
>> Long lists just waste storage, and on the Internet, they just waste
>> bandwidth."
>
>I keep my list up to 2^32 on disk, even though I think it would be faster
>to generate them. (At some point it becomes slower to generate them.) The
>reason I do that rather than generate them each time is for
>reliability. If I'm looking at primes of a certain type, I read them in
>and check. I think this is saver than changing the generating program each
>time. Also the program to read them in is a lot shorter and less prone to
>error than the generating program.

I've got something similar on my website - a short description of
primes, with C source to programs to generate and read primes in a
successive-differences format. My format uses four bits to store the
difference between the majority of primes under 2^32 (and multiples of
four bits for the rest). For this range, the file format takes an average
of about (I forget the exact numbers) five bits per prime.
I heard and read several places that it's faster to generate primes
in RAM with a sieve than to read them from a file, which I never
understood, because my programs read the disk format and recreate
the primes in about half the time it takes to generate them in RAM.
One caveat, the programs don't work well with numbers near 2^32. :(
-----
• At 03:16 PM 3/5/2001 -0500, Ben Bradley wrote: I heard and read several places that it s faster to generate primes ... It is up to a point, and that point
Message 6 of 8 , Mar 5, 2001
At 03:16 PM 3/5/2001 -0500, Ben Bradley wrote:
I heard and read several places that it's faster to generate primes
>in RAM with a sieve than to read them from a file,

It is up to a point, and that point depends on the speed of your CPU and
disk drive. Reading from the file is pretty much linear in the number of
primes, which is sub-linear for primes below a limit, whereas a sieve is
super-linear, so for large enough numbers, the sieve will take longer. On
my machine, reading primes < 2^32 from disk is about twice as fast as my sieve.

+--------------------------------------------------------+
| Jud McCranie |
| |
| 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
+--------------------------------------------------------+
• A carefully constructed dump of a sieve will beat most run-length compression schemes, even with huffman (or other entropy) compresion. For broad ranges, I d
Message 7 of 8 , Mar 5, 2001
A carefully constructed dump of a sieve will beat most run-length compression schemes, even with huffman (or other entropy) compresion.
For broad ranges, I'd use a 480/2310 comb to the sieve.
For small ranges (a million primes) a 8/30 comb is fine.
With the right code, I guestimate that generating primes should be faster than reading them off disk still, but it's not by a huge margin. Race Dan Bernstein's Primegen and Eratspeed against your hard disk for primes up to a billion if you don't believe me. (there are links on the primepages)

However, my current sieving job is generating 17 digit numbers, and I store the deltas, which average around 7-8 digits. This gives me roughly 2:1 compression. I then BZIP2 them, which gives an almost exact log(10)/log(256) ratio, as the numbers are essentially unpredictable. Even then, I think I could fill a CD in a month.

Twins fall into this latter catagory, and their density means that hard disk storage is worthwhile.

Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
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