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Ice9 2003-12-22 14:30

Who has a list?
 
While not completly mersenne related, I was wondering who keeps a list of all known primes. I understand that the list would be way too big to easily distribute, but are there people or organizations that are recognized to have the entire list? I coudn't even find a reference to who might have such a list. Also, does anyone here know of any lists avaliable in the 90 to 100 digit range?

Thanks

only_human 2003-12-22 17:47

In my opinion the best place to look is Prime Pages maintained by Dr Chris Caldwell. The is an extremely good site that is very rewarding to read on many levels. As far as prime lists go this is the page on that site: [URL=http://www.utm.edu/research/primes/lists/]Lists of Primes at the Prime Pages [/URL]
In this information is a list of the 5000 largest known primes, a list of small primes and others. In the small prime list are some 110 to 200 digit primes (and many others too)

I defer to others here concerning questions about entire complete lists of primes.

ewmayer 2003-12-22 20:41

Any list of the actual [b]primes[/b] below some bound B grows exponentially fast with the number of digits in B (i.e. with log B, where the log is to any base), so such lists are not generally kept, as it is faster to simply generate said primes when needed and only explicitly store the ones that are needed at the moment. We know that the number of primes < B scales as B/ln B (natural log here), so e.g. below 2^32 (rouhgly 10^10) we have nearly 2^28 primes, each of which would need ~4 bytes to store explicitly, for a total of roughly a Gigabyte. There are ~10^98 primes < 10^100, which is vastly more than the number of elemntary particles in the known universe. What people [b]have[/b] done along these lines is to actually [i]count[/i] the number of primes below some ever-increasing bound, to check the accuracy of various asymptotic formulae which approximate the prime-count function. At present, the prime count has been exactly enumerated to slightly above 10^20, so 10^100 is a long way off! Remember, actual enumeration requires on the order of as many CPU-cycles as primes, and in all of human history there have been just slightly above a mole (6.23...X 10^23) of CPU-cycles. Even were this count to double each year, it would take over 300 years to reach 10^100.

Here are some related links from MathWorld:

[url]http://mathworld.wolfram.com/PrimeNumberTheorem.html[/url]

[url]http://mathworld.wolfram.com/PrimeCountingFunction.html[/url]

Reboot It 2003-12-23 00:51

[QUOTE][i]Originally posted by ewmayer [/i]
[B]... and in all of human history there have been just slightly above a mole (6.23...X 10^23) of CPU-cycles.[/B][/QUOTE]I know this doesn't alter the argument, but, just for the record, Avogadro's constant is actually reckoned to be 6.[b]0[/b]2214199 x 10[sup]23[/sup]. See for example the National Physical Laboratory website's useful [URL=http://www.npl.co.uk/reference/fundamental_constants.pdf]PDF reference guide to fundamental physical constants and conversion factors[/URL].

I only point this out because if I don't, somebody else will (honest!). :grin:

ewmayer 2003-12-23 15:40

[QUOTE][i]Originally posted by Reboot It [/i]
[B]I know this doesn't alter the argument, but, just for the record, Avogadro's constant is actually reckoned to be 6.[b]0[/b]2214199 x 10[sup]23[/sup].[/B][/QUOTE]

Thanks - can you tell I'm a long ways removed from my college chemistry courses?

I know this doesn't alter the argument, but, just for the record, it's really the [i]Loschmidt[/i] constant, as Avogadro never made any estimate of the number itself. :wink:

[url]http://gemini.tntech.edu/~tfurtsch/scihist/avogadro.htm[/url]

Reboot It 2003-12-23 19:44

Touché! :bow:

frodsham 2003-12-29 19:35

[QUOTE][i]Originally posted by ewmayer [/i]
[B]I know this doesn't alter the argument, but, just for the record, it's really the [i]Loschmidt[/i] constant, as Avogadro never made any estimate of the number itself.[/B][/QUOTE]
Not really, because if you read

[QUOTE][i]Originally posted by Reboot It [/i]
[B]See for example the National Physical Laboratory website's useful [URL=http://www.npl.co.uk/reference/fundamental_constants.pdf]PDF reference guide to fundamental physical constants and conversion factors[/URL].[/B][/QUOTE]
you'll find
[QUOTE]Loschmidt constant (Na/Vm) ~= 2.686 7775 x 10^25 m^-3[/QUOTE]
The "mistake" was to call it Avogadro's constant rather than [the] Avogadro constant.

Mathematical pedantry can be such [b][i]fun[/i][/b].

frodsham 2003-12-29 19:53

[QUOTE][i]Originally posted by frodsham [/i]
[B]Mathematical pedantry can be such [/b][i]fun[/i][b]. [/B][/QUOTE]
And, moreover, Avogadro was 21.5 times better than Loschmidt. When I was young that was the density of Platinum, though it isn't now.

(The ratio of relative uncertainties in the 2 constants.)

ewmayer 2003-12-30 15:28

[QUOTE][i]Originally posted by frodsham [/i]
[B]Mathematical pedantry can be such [i]fun[/i].[/B][/QUOTE]

Would this discussion best be characterized as mathematical or nomenclatural pedantry? Is it pedantic of me to ask that?

mfgoode 2004-01-27 16:32

Who has a list?
 
[QUOTE=Ice9]While not completly mersenne related, I was wondering who keeps a list of all known primes. I understand that the list would be way too big to easily distribute, but are there people or organizations that are recognized to have the entire list? I coudn't even find a reference to who might have such a list. Also, does anyone here know of any lists avaliable in the 90 to 100 digit range?

Thanks[/QUOTE]
Try this website out and click on HOW MANY.

[url]http://www.utm.edu/research/primes/mersenne/index.html[/url]

Mally :yucky:


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