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-   -   What is the largest database of all primes from 2 up? (https://www.mersenneforum.org/showthread.php?t=5270)

jasong 2006-01-03 00:34

What is the largest database of all primes from 2 up?
 
I thought I'd give you this question to chew on: If you start with 2 and find all primes in order, what is the biggest known database of this type?

I don't know the answer and I'm not sure how it would be discovered.

I would also be interested in people's opinions of how big a hard drive you would need to store all the primes from 2 to, say, 2^100 in uncompressed form with a byte between them.

Xyzzy 2006-01-03 00:45

[quote=jasong]I would also be interested in people's opinions of how big a hard drive you would need to store all the primes from 2 to, say, 2^100 in uncompressed form with a byte between them.[/quote]
[url]http://www.mersenneforum.org/showthread.php?t=3861[/url]
especially post #9

[URL="http://www.mersenneforum.org/showthread.php?t=1768"]http://www.mersenneforum.org/showthread.php?t=1768[/URL]

Richard Cameron 2006-01-03 20:54

[QUOTE=jasong]I thought I'd give you this question to chew on: If you start with 2 and find all primes in order, what is the biggest known database of this type?
[/QUOTE]

this one, perhaps?

[URL="http://www.prime-numbers.org/"]http://www.prime-numbers.org/[/URL]

on a related topic, a friend asked me a while back what is the smallest number whose prime/compositeness is unknown. I think the question although seemingly sensible, doesn't have a simple, sensible answer.

Richard

akruppa 2006-01-03 21:35

There isn't much point in storing a list of prime numbers. They can be generated much more quickly than such a list could be transferred over a network. Look for Bernstein's primegen library, afaik it can generate primes up to about 10^18. There are about 24*10^15 primes below 10^18, so keeping them in a database is out of the question.

Alex

jasong 2006-01-04 01:30

[QUOTE=Xyzzy][url]http://www.mersenneforum.org/showthread.php?t=3861[/url]
especially post #9

[URL="http://www.mersenneforum.org/showthread.php?t=1768"]http://www.mersenneforum.org/showthread.php?t=1768[/URL][/QUOTE]
I really should've given more thought to this:

x/log x gives the answer of about 3.33333...^29th power.

Assuming a terabye is 10^12, that means it would take 1/3rd of a mega-tera-terabye. Now assuming a square inch can take up a gigabyte(which I don't believe has actually happened yet, but probably will), the hard drive would take up 3.333...*10^20th power inches, which means
2.31...(481 repeated 5 times)...4*10^18 sq. feet, or 83032556201 sq. miles. The United States has an area of 3,619,969 sq. miles, which means the hard drive would cover a little more than 22937 United States.

I was unable to find the sq. mileage of the earth, with or without water in my dictionary.

Would anyone like me to calculate how fast the edge of this hard drive would spin at 7200 rpms, lol?

Edit: error, I assumed every number took up a byte, but most of them are too big.

Numbers 2006-01-04 19:04

[QUOTE=jasong]Would anyone like me to calculate how fast the edge of this hard drive would spin at 7200 rpms, lol?[/quote]
Assuming that the edge of the disc would be travelling at faster than light speed (which we know is not possible, but just assuming) that would mean that data sent to memory locations near the edge of the disc would never arrive! Lol :o)

cheesehead 2006-01-04 23:16

[quote=jasong]Now assuming a square inch can take up a gigabyte(which I don't believe has actually happened yet, but probably will), the hard drive would take up 3.333...*10^20th power inches, which means
2.31...(481 repeated 5 times)...4*10^18 sq. feet, or 83032556201 sq. miles. The United States has an area of 3,619,969 sq. miles, which means the hard drive would cover a little more than 22937 United States.[/quote]... or, more practically, it could have 11469 two-sided platters, each of which is only 1 United States in size.

[quote]I was unable to find the sq. mileage of the earth, with or without water in my dictionary.[/quote]Surface area of a sphere of radius r = 4*pi*r[sup]2[/sup].

Mean radius of Earth is 3960 miles => ~2*10[sup]8[/sup] sq. miles surface area.


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