mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2006-01-03, 00:34   #1
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

DB116 Posts
Default 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.
jasong is offline   Reply With Quote
Old 2006-01-03, 00:45   #2
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

2·3,931 Posts
Default

Quote:
Originally Posted by 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.
http://www.mersenneforum.org/showthread.php?t=3861
especially post #9

http://www.mersenneforum.org/showthread.php?t=1768
Xyzzy is offline   Reply With Quote
Old 2006-01-03, 20:54   #3
Richard Cameron
 
Richard Cameron's Avatar
 
Mar 2005

2528 Posts
Default

Quote:
Originally Posted by 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?
this one, perhaps?

http://www.prime-numbers.org/

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

Last fiddled with by Richard Cameron on 2006-01-03 at 20:54
Richard Cameron is offline   Reply With Quote
Old 2006-01-03, 21:35   #4
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

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
akruppa is offline   Reply With Quote
Old 2006-01-04, 01:30   #5
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5×701 Posts
Default

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.

Last fiddled with by jasong on 2006-01-04 at 01:38
jasong is offline   Reply With Quote
Old 2006-01-04, 19:04   #6
Numbers
 
Numbers's Avatar
 
Jun 2005
Near Beetlegeuse

22·97 Posts
Default

Quote:
Originally Posted by jasong
Would anyone like me to calculate how fast the edge of this hard drive would spin at 7200 rpms, lol?
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)
Numbers is offline   Reply With Quote
Old 2006-01-04, 23:16   #7
cheesehead
 
cheesehead's Avatar
 
"Richard B. Woods"
Aug 2002
Wisconsin USA

11110000011002 Posts
Default

Quote:
Originally Posted by 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.
... 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.
Surface area of a sphere of radius r = 4*pi*r2.

Mean radius of Earth is 3960 miles => ~2*108 sq. miles surface area.
cheesehead is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Largest k*2^n-1 Primes in 2011 Kosmaj Riesel Prime Search 0 2012-01-01 16:52
Largest k*2^n-1 Primes in 2010 Kosmaj Riesel Prime Search 0 2011-01-05 04:24
Minimum primes of various forms database? jasong Information & Answers 1 2007-11-01 01:58
Largest range between primes? Unregistered Math 10 2006-08-21 19:54
Largest Simultaneous Primes robert44444uk Octoproth Search 4 2006-02-04 18:45

All times are UTC. The time now is 12:42.

Tue Dec 1 12:42:50 UTC 2020 up 82 days, 9:53, 1 user, load averages: 2.72, 2.75, 2.58

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.