Welcome message





About us
15k, is a group of people that searches for prime numbers, using their own personal computers.
It's now easy for anyone to win the E.F.F.'s(Electronic Frontier Foundation) prizes.
You don't have to be a number theorist to find primes anymore! Discovering smaller primes can be fun and helpful too!
Here are some members that have already found huge primes. We hope to be the first to find a large enough prime,
to win the $150,000+ prize, by using the fastest software to do this, called RMA.NET.

Goals
To find titanic prime numbers, of the form k*2^n(-+)1 as quickly as possible with RMA.NET.
Follow the prime directive and boldly go, where no-one has gone before. Win $150,000 or more!





Advantages
It's completely free, there is no agreement necessary.
The actual processor time is counted, utilized and displayed.
Searches of the Riesel form are faster than the Mersenne form.
A complex and hard to model process, is now automated in one click.
The adaptive behavior of the program saves processing time, that would otherwise be wasted.
There's no use of vulnerable network components, that could compromise the security of your potential prize candidates.
The user can customize their own sounds and voices, when certain main events occur.
The number of primes, and the number of digits are displayed, onscreen.
You can see and hear, what the probability is that you have a prime, within the file that you are testing.


Download version 1.7 now! (Multi-core version coming soon)
Requirements 2000/XP/Vista Microsoft 2.0 .NET framework
My personal friends, can just ask me for an RMA CD.

You can download and install RMA now for free, by clicking this setup.zip.


http://www.mediafire.com/file/hmjdww0doqb/setup.zip



What to do next?
First you'll need to prove a titanic prime!
When RMA loads for the first time, click start and you'll will be asked if you want to choose parameters at random.

If you want to test larger primes, for the $150,000 prize, then click no. Then click yes on the next message prompt.

Let RMA run for several weeks 24/7, while checking on it's progress daily.
A range of larger primes make take several months to finish.
When you find your first prime, send Chris Caldwell an email here. Inform him that you need a new prover code.
Submit your prime number to him. List all the programs you used to find the prime. Tell him that you found it as a member of 15k. Subsequent primes should be submitted here, or you can use RMA's menu link to open the submit page.

Details
The help contents of NewPGen it states:
"In general, you ought to sieve until the rate at which NewPGen is throwing out composites is equal to the rate at which Proth/LLR/PFGW can perform a primality test on the numbers. Actually, you should stop a little sooner - the idea is to find primes, after all."
(Paul Jobling)
The E.F.F's resource says that:
"The Mersenne test for 2^n-1 is the fastest known primality test for a given large numbers.
However, it is faster to search for primes of the form k*2^n-1."
RMA.NET automates this entire process for you, by monitoring the progress, and when necessary merges the two files. The priority is then changed to the most efficient rate. RMA.NET runs on only the idle cycles, which are not being used by your PC, so your computer will not become sluggish. These idle cycles would normally be a waste of electricity, since they are not being used. In a way it's a form of recycling waste energy, while giving you the chance to win a sizable prize.

Help
Advanced panel view:

1. This is the parameter for the multiplier k.
2. This is the main button to start or stop the search.
3. This is the parameter for the exponent n.
4. This is the main work folder, that contains RMA's files.
5. This is the merged file, that contains remaining candidates.
Click to view. Right-click for more file options.
The number below the file, is the name of the file, that contains iterative information about incomplete tests.
You can even check to see what the chances are that you have a prime.


6. This is the information about running processes.
7. This shows the activity level of the sieving and testing processes.
8. This is the number of primes found, and the number of digits of the last one found.
9. This is text where the primes are printed.
10. This the parameter for the number of candidates to search.
11. This is the advanced panel button for intermediate-advanced use.
12. This is the checkbox to indicate that there is work pending.
13. This is the text file to write the parameters for the work to do file.
You must specify the k & n & total number of candidates, one line at a time.
For example this line:
2145 110503:10000
This will use k=2145 n=110503 c=10000, as the parameters, for whatever form is chosen.
You may specify as many lines(ranges) as you like.
14. This is the checkbox to indicate that voices are to play when big events happen.
15. This is the text file to write the text, that you want recited.
Three major events can be vocalized, and should be written as:
PrimeFound=YourTextToReciteHere
StageEnded=YourTextToReciteHere
RangeEnded=YourTextToReciteHere
16. This is the checkbox to indicate that sounds are to play when an event happens.
17. This is the text file to write the file path, of the sounds you want played.
Three major events can play sounds, and should be written as:
PrimeFound=C:/Windows/Media/Windows Notify.wav
StageEnded=YourSoundFilePathHere
RangeEnded=YourSoundFilePathHere
18. This is the volume control trackbar.
19. This is the highest prime used in the sieve.
20. These are the rates of time for, sieving, testing, and prime finding.
21. This is the refresh button. It can update the times manually. during periods of inactivity.
22. This is the number of remaining candidates.
23. This is the current number being tested.
24. This is the stage indicator.
25. This is the progress bar.
26. This is the percentage that has been completed so far, and the estimated completion time remaining.


To Create a new file, click on the main File menu. Then press the main start or stop button, to resume or pause the process.
Advanced users can continue an old file manually, that has not been started with RMA, by using the second option.



You can set RMA to start up when windows starts.



You can minimize RMA as a tray icon, and still view the current progress, by hovering the mouse over the taskbar icon.



You can right click on RMA's tray icon, to change file menu options.



You can click on a control, to hear Microsoft's speaking voice, tell you more details.


You can also maximize the main window, when in advanced view, to show NewPGen and LLR at work.
This is usually used for diagnostic purposes only.


If you have any questions, post a topic in this group, or drop me an email here.


History
The 15k search became the first popular sub-project in 2003 after the release of LLR in late December of 2002.
We held the number one position, until recent times. Our lead was due to this mathematical advantage:
"In general when k has many small factors, n is more likely to produce a prime because it can't have those same factors."
Since 3, and 5 are both primitive roots modulo 2, they were chosen as the base multipliers, so that the symbolic form itself eliminates a large field of potential factors, without over limiting the potential range of candidates k. Currently we are focusing on fixed n candidates, which are faster than fixed k searches.

Math of LLR(written by Jean Penne)
Jean writes,
The algorithm used by LLR is a generalization of the Lucas-Lehmer algorithm, used to test the primality of the Mersenne numbers. I name this algorithm the Lucas-Lehmer-Riesel algorithm because it is explained and demonstrated in an article by Hans Riesel : "Lucasian Criteria for the Primality of N=h*2^n-1" Mathematics of Computation, Vol. 23 108, pp. 869-875, Oct. 1969
The main theoretical fact is contained in the Theorem 5 (Lucas'Criteria for h*2^n-1) : Suppose that n=2, h is odd
A =( (a+b*sqrt(D))^2)/r, Jacobi(D,N) = -1, and Jacobi(r,N)*sign(a^2-b^2*D) = -1.
Then, a necessary and sufficient condition that N shall be prime is that u(n-2) == 0 (mod. N)
if u(n) = u^2(n-1) - 2 with u(0) = A^h + A^-h. How to use that ?
The number u(0) can be computed using a well known recursion formula : v(0) = 2, v(1) = A+A^-1, v(k) = v(1)*v(k-1) - v(k-2).
So, we obtain u(0) = v(h). The remaining problem is to found a value for v(1) .
The numbers A and A^-1 are units of the quadratic field K(sqrt(D))(that is to say units of the ring of the integers of this field...). So, they are powers of the fundamental unit of the field. Instead of choosing a square free integer D and searching for units satisfying the conditions of theorem 5, Riesel takes increasing values for v(1), and, remarking that A and A^-1 are the roots of the equation :
A^2 - v(1)*A + 1 = 0 computes D as the square free part of v^2(1) - 4.
It remains to verify that the resulting D, a, b and r values satisfy the conditions of theorem 5.
The value of v(1) so found is the smallest possible.
Regards,
Jean.

Math of RMA(written by Shane Findley)
Here is a link to the sequence, mathematically speaking.
Let t(x) be the highest power of 2 which divides x+1.
Then a(1)=3; a(n) is the least prime for which t(a(n)) > t(a(n-1)).
Example: a(5)=1279, because t(a(4))=7, and 1279 is the least prime with t(a(n))>7.
Heuristic proof of the infinitude of Mersenne primes: If there were to be a finite number of Mersenne primes, then the minimum k, of possible least primes would be forced into absurdity with k=>3.
Hence, the number of Mersenne primes must be infinite, because there are an infinite number of Riesel-Mersenne primes with k=1.