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2003-11-19, 18:56
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#1 |
Aug 2002
22×5×13 Posts |
Readme First - (for the Public Forum)
I appologize in advance for the long posts following this one. I have put together something - that with a bit of help from you guys - can be used as a locked sticky in the Public Forum.
Please give feedback (good and bad), comments, corrections etc. Thanks  PM |
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2003-11-19, 18:57
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#2 |
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Aug 2002
4048 Posts |
Welcome
Welcome to the mersenneforum.org, the official forum for The Great Internet Mersenne Prime Search (GIMPS) project. The purpose of this thread is to give new users some information about the project, links to more information, how to get started, where to get help and other useful information. A little bit of history Prime numbers have long fascinated amateur and professional mathematicians alike. In the past fifty years a number of individuals wrote software and developed databases to aid in the search for Mersenne primes. Starting in late 1995 George Woltman gathered up the disparate databases and combined them into one. In early 1996 George placed this database, and a free, highly optimised program for search for Mersennes onto the Internet to coordinate the search; the start of The Great Internet Mersenne Prime Search. GIMPS seeks new primes, while also seeking to factor the composite Mersennes and double (and triple) check previous results. When the project began, there were only 40 people and a little over 50 computers using their spare CPU cycles; the project has since grown to thousands of users and computers. The software has also changed quite a bit from GIMPS's beginnings; The factoring part of the program was originally written for 386 computers, in its current incarnation it has hand-coded support for the P4s SSE2 codeset. Another aspect of the software, which probably influenced how the project is set up and managed is that at first, there were many errors in checking for the primes, and all discovered Mersenne primes had to be double-checked to ensure their validity. Even today every result, whether a prime or not, is double-checked, as errors are still occurring. Current estimates is that the error-rate is actually increasing slightly. GIMPS is a unique distributed computing project for many reasons. George Woltman publishes the GIMPS software source code, and welcomes anyone to revise the software or make enhancements, as long as they follow the GIMPS rules. And, although the source code has been fully released, there doesn't seem to be any threat of data contamination that is present in some other distributed computing projects. If the results indicate a prime number, other users could check the same exponent and verify that it is a Mersenne prime, and given the prize and fame a discoverer gets, it seems unlikely that someone who found a Mersenne prime would keep the discovery hidden. A bit of theory An integer greater than one is called a prime number if its only divisors are one and itself. The first prime numbers are 2, 3, 5, 7, 11, etc. A Mersenne prime is a prime of the form 2^P-1. The first Mersenne primes are 3, 7, 31, 127, etc. Mersenne numbers are named after the French monk Marin Mersenne (1588-1648). Mersenne investigated prime numbers and he tried to find a formula that would represent all primes. Although he failed in this, his work on numbers of the form 2^P-1 where p is prime, has been of continuing interest in the investigation of large primes. Mathematicians claim it is easy to prove that if the number n = 2^P-1 is prime then p must be a prime. In 1644 Mersenne claimed that n is prime if p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 but composite for the other 44 primes smaller than 257. Over the years it has been found that Mersenne was wrong about 5 of the primes less than or equal to 257 (he claimed two that did not lead to a prime (67 and 257) and missed 3 that did: 61, 89, 107). The Mersenne primes are not just pretty numbers, though: they do have many applications. The most common uses for these primes are for forming algorithms, and, interestingly enough, To test the hardware To show that a small number is prime, we can just divide by the primes below its square root. For example, 53 is prime because it is not divisible 2, 3, 5 or 7. Large numbers need more complicated tests that usually involve a form of LaGrange's theorem. If you look at a list of the largest known primes you will see that for most such number n, either n+1 or n-1 factors easily. Mersenne primes follow this rule and are the primes of the form 2^P-1. It is easy to show that p here must also be a prime, (at least that is what the mathematicians are saying). Because of the special form of the Mersennes, there is an easy test to see if they are prime, called the Lucas-Lehmer test. The Client Prime95 is a free program written by George Woltman and provided on his GIMPS site. Just download the software, install it, and let it run. Simple and easy, but the road is long. GIMPS is not a project for the faint at heart, most of the exponents (work units), depending on type of work you choose to do, are huge!. Over 86% of those who have begun to test a Mersenne exponent with GIMPS have never completed even one, and the average GIMPS participant has completed less than three (mean 2.67). Two types of work are done under GIMPS, trial factoring and Lucas-Lehmer testing. GIMPS appeals to those with a lot of patience, the work units take a lot of crunching, but pack serious punch. Very friendly to offline operation and P4's but runs well on a wide range of x86 machines. Finding a Mersennes prime is no easy task, a first time primality test for a single candidate exponent takes a fast machine three to four weeks, running 24/7, on the fastest Tbirds/PIII's, P4's perform better, due to the SSE2 optimizations in the code. This is without a doubt this is the one of most intensive operation in all of computing. A test runs through three phases before the result is considered final, done gradually and by several different machines. First, each candidate exponent goes through a level of trial factoring, which is a brute force approach designed to eliminate non - prime candidates early on in the process. This works by checking the number for small divisors, using the fact that factors of Mersenne numbers are of the special form q = 2kp+1, and that testing a factor candidate simply requires a binary powering, i.e. one finds 2^p modulo q (which involves roughly log2(p) arithmetic steps on numbers no larger than q^2) and checks if the result is equivalent to -1 modulo q. One can also do a small amount of factoring work using (say) Pollard's p-1 method or the elliptic curve factorizations method, both of which involve manipulating numbers the size of the Mersenne number itself. If no factors are found then the exponent is released for a first time Lucas - Lehmer primality test. A final double-check is done later by another computer to verify the validity of the result. This project has it advantages, namely the client itself. This has to be the most stable, mature, feature rich DC client on the net. It will use as much or as little or much memory as you allow it, and will get completely out of the way whenever another program needs cycles. It can be run as a service and completely hidden for view as well as the ability to run when the user logs off so no lost cycles to waste. [list=1][*]Mature client[*]Easily runs when logged off. Just check Run at Bootup. You need not know about Windows services![*]Caches work so it keeps going if offline. No helper programs are needed to cache work for it.[*]Low memory needs so PCs with modest RAM can use it. If you are short on RAM you can still run it. (2% of the time it wants more RAM for P-1 and user can set limit.)[*]Low bandwidth needs: <~1 KB / month. Great for dial-up![*]Stringent verification within each run and across runs, so you know your CPU cycles are not being wasted.[*]GIMPS offers something that many other distributed projects don't: actual regular discoveries[*]A very responsive developer, George Woltman, who frequents this board as Prime95[/list=1] Monetary Awards The Electronic Frontier Foundation is offering a $100,000 award to the first person or group to discover a ten million digit prime number. If you find such a prime with the software provided, GIMPS will claim the award and distribute the award according to the rules published on the GIMPS site. Disclaimers: If you decide to install this client, or any other DC client, on your employers machines, always, always get written permission before installing idle-cycle software on any machines you do not have absolute administrative control over. Many companies have a strict policy against running any non-business software. You will not get a lot of sympathy from the DC community if you installed a DC client on a lot of machines and then got into trouble because of that. It could actually be a criminal offence. One thing that people running work machines should be aware of is the prize money involved, $55k if you find a 10 million digit Prime number so there could be some conflicts of interest here. Continues in next post...... Last fiddled with by garo on 2003-11-20 at 01:19 |
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2003-11-19, 18:58
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#3 |
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Aug 2002
22·5·13 Posts |
......continued from previous post.
The type of work units you can do[list=1][*]Factoring of a prime number (exponent) candidate This is a precheck of a candidate exponent. These work units take the least time and are given out by the server according to your cpu speed. They may go through several iterations of bit length before clearing and getting sent to a fast machine for the more intensive Lucas-Lehmer testing. This is best for low-end PIIIs and Athlons[*]Doublechecking a prime candidate Doublechecking is done to work units which have cleared one round of LL testing. This verifies that the LL test has concluded correctly and ensures that the cpu of first running conformed to spec. These are small to medium units, PIII, Athlons and low end P4s turf here. Basically this is a Lucas Lehmer test, but the exponent size is smaller than for the current first time primality test range. [*]Lucas Lehmer (LL) testing on a prime candidate These candidates are much bigger than the run in the double testing pool. It is a virgin run; the chance of finding a prime candidate is about 1 in 100 000. Prefactoring ensures that no time is spent on lengthily LL work when a simple factor is present.[*]10 000 000 + digit Mersenne prime LL testing This is the grand daddy of all DC WU - only the diehard crunching fanatic need apply. Depending on the size and your box, several months to a year (and even more) of cpu time is needed. Same as above except for size and one other thing: the prize. Find one of these and you win a substantial prize, something like over 55.000$ US$ - enough to cover a good bit of D. Find the first one and you will live forever in mathematics history.[/list=1] Statistics WU credit is in based on P90 cpu hours. If you have a faster box you get more P90 hours. Simple and unchanging. The stats server is constantly updated - turn in a wu and get instant credit. No bullshit here. How to start with GIMPS Step 1 Download the appropriate program for your OS.
Step 2 If you downloaded p95v237.exe then run it. Ghost Installer has generously made their setup program free for all. Thus, you can run the prime95 setup program and simply follow the instructions to install Prime95. All other platforms will need to create a directory and decompress the file you just downloaded. Windows users can choose from a variety of decompression programs. Some are PKZip, WinZip, or dozens of others at Tucows. Linux and FreeBSD users should use the standard tar and gzip decompression utilities. Step 3 Read the readme.txt file for more detailed instructions. Generally, joining GIMPS is as simple as running the program, answering a few questions, and the program does the rest. It contacts a central server to get some work to do. There are several ways to set up the program to run every time you restart your computer. You can track your progress on a stats page the server updates every hour. Step 4 Questions and problems. Consult the readme.txt file for possible answers. You can also search for an answer, or ask for help in the GIMPS forums. Otherwise, you will need to address your question to one of the two people who wrote the program. Networking and server problems should be sent to Scott Kurowski, but please consult his FAQ first. Such problems include errors contacting the server, problems with assignments or userids, and errors on the server's statistics page. All other problems and questions should be sent to George Woltman, but please consult his FAQ first. Note : It is important to show a bit of patience if you get any problems with registering or requesting work. The main server, www.mersenne.org, has had some availability problems of late. If you do get problems, please check with the forum for the current status. How to set up a Team If you want to set up a team, for you and your friends, you will have to specify this when registering from one of your clients. All members of your team will use the same UserID and password, whereas each computer will get its own ComputerID. The "create a team ..." Checkbox is used to ensure that UserID and password can't be changed by team members, whether intended or not. Each computer gets its individual tasks and can individually be set to special task types under "Test, PrimeNet". Besides possible psychologic effects of competition, building a team has no impact on how soon a task is done. Nevertheless, building or joining a team can be fun, as you get in contact with other people, can find friends and equal-minded people that shares the same interests as you. Some GIMPS teams
Information sources Some sources of information that you might find interesting |
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2003-11-19, 19:52
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#4 |
Aug 2002
London, UK
5·19 Posts |
Just a little note - there needs to be a [close bold] (obvously I can't type the code here properly!) in the Welcome paragraph, as the emboldened text continues right through into the history section.
Otherwise this looks excellent! Well done. |
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2003-11-19, 20:00
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#5 |
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Aug 2002
10416 Posts |
I saw the missing [ / b ] , but it was too late to fix the post. Thanks for the comment.
 I've also fixed up some of the headings. Is it too long for somebody looking for information about the project ? PM |
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2003-11-19, 20:10
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#6 |
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Aug 2002
London, UK
5·19 Posts |
There are also a handful of minor (and pretty insignificant!) typos, and I would be happy to offer to correct them offline (i.e. by exchanging a Word document or whatever) if you would like me to - this might be seen by loads of people!
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2003-11-19, 20:17
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#7 |
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Aug 2002
4048 Posts |
Yes please
I have it as a text file ready to be posted to the board, ie with vB code and all that. I'll send the file to you. And Thanks
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2003-11-20, 01:56
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#8 |
Aug 2002
110010002 Posts |
The link to George's FAQ page is invalid.
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2003-11-20, 03:25
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#9 |
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Aug 2002
1000001002 Posts |
The Link to George's FAQ is OK, but the one to the mailinglist is not. I thought I tested themm all, but this is why I ask for comments and corrections
.I would like to provide a valid link to the Mailinglist FAQ, so if anyone has got it could they please post it here. Some other comments that I have received in private messages were very useful. I have decided to add two things to the start of the piece of text.  [list=1][*]A table of Contents[*]An executive summary (if I can write one) [/list=1] PM |
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2003-11-20, 03:37
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#10 | |
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Aug 2002
23·52 Posts |
I still get a "The page cannot be displayed" error when I click on the George Woltman FAQ link. It's trying to take me to "http://faq.htm/", which can't possibly be correct.
Quote:
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2003-11-20, 03:43
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#11 |
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Aug 2002
22×5×13 Posts |
 You are right. I thought you meant the links at the bottom. I will fix that right away in the text. Thank you PM |
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