please explain this project

[jasong]

I apologize in advance, but there were some references on the explation page that were confusing to me.

2^n-1 always getting odd numbers I understand, the rest of the stuff confused me. There were some 6-7 digit numbers on the page, but I didn't understand the explanation of how they were obtained. Also, while I may have taken a class involving little symbols down and to the right of a letter or number, I've forgotten what they mean.

I've passed college algebra, have a 130 IQ, and believe I can learn anything if given time, good educational materials, and maybe some help.

Could someone please point me in the right direction in understanding this?

[b2riesel]

Hello jasong,

It is all a bit overwhelming at first glance to make sense out of everything. From the information you gave, I'm not quite sure which pages you were talking about. But let me explain a few things that may help and if they don't, you can always email me, make a forum post on my forums asking for help, drop by our IRC channel and ask me in real time, or various other ways. I'm usually pretty quick getting back with people.

First, what exactly are we trying to do?

Seems Hans Riesel noticed that when using the following: k*2^n-1 you can pretty easily get a prime number quickly for MOST numbers that you feed into the equation for k. Now what is n you ask? Well any integer to infinity that you want. So you can do k=3 and n=whatever. 3*2^4-1 for example. You do the power first of 2^4 or 2*2*2*2 and we get 16. Now to the multiplication stage of 3*(2^4) or 3*16 and we get 48. Now the final part of the equation to subtract 1 to get 47. So, we have 3*2^4-1 is 47 for a nice little prime.

Most odd numbers you put in for k will hit a prime pretty quickly if you try enough n values.

However, Ole Hans noticed that SOMETIMES and VERY rarely you can put in a k value that will never....ever....ever...ever hit a prime number no matter how many n values you try. From 2 to infinity you can just hold your breath and pass out because you will never see a prime. He noticed that the first k to do this in his opinion was k = 509203. That being said 509203*2^n-1 will never ever ever ever find a prime number...no matter what you stick in for n. He then conjectured that k = 509203 was the smallest k to display this quality. Saying in essence that all odd integer k's below k=509203 would find a prime number.

Now Wilfrid Keller about a decade or more ago started an effort to prove this conjecture. Now called the 'Riesel Problem' and proving that k=509203 was the smallest 'Riesel Number'. Years of hard work by numerous individuals went thru the other 250000+ odd values of k to find them prime and discard them as possible 'Riesel Numbers' that were smaller than k=509203. At first the search went very fast. K=3 as I showed didn't last long and k=5,7,9,11,13,15 and so on quickly fell because they easily produced a prime number.

Now...here we are over a decade later after Wilfrids Search...which began a half lifetime after Hans Riesel made the Conjecture(1956). Some k's were found prime using pen and paper, and some later found using individual computers with Wilfrid's search.

Now comes RieselSieve. We started out as an effort to help the others by sieving all the k and nvalues at one time so that individuals could concentrate on finding primes and less time sieving. Sieving is where you find factors for all the numbers that you need to test...before you test them for prime. If you know that k*2^n-1 is divisible by 3...why bother testing it? That is what our sieve does...we find factors for the possible prime numbers so they don't have to be tested for prime. That may be the numbers you see on our site like "Sieving Complete to 75T"...or...basically we are saying that we have divided all the k values with n values from 2 to 20 million...by all the numbers between 2 and 75,000,000,000. Yep...that's a LOT of numbers.

The other numbers you will see is our list of 101 k's. This was the amount of k values that remained when I started this project. Each time we find a prime we eliminate that k value. We only need to find one prime per k to prove that it couldn't be a Riesel K...or a k that can never ever ever produce a prime number...because hey...we just proved it will find a prime.

Out beside the k values you may see n's remaining...or how many n values between 2 and 20 million we have left to test for prime that escaped the allmighty sieve. And you will see an nmaxtested. This means we have tested EVERY n value below this value. If the nmaxtested is say.... 1160000 for k = 2293...that is saying that every test below 2293*2^1160000-1 has either been tested for prime...or a factor has been found that divides that number using the sieve.

Hopefully this has answered a few of your questions. Pardon me if I made a few typos. This was a post made on the fly and not a cut and paste from some other page. If you have any further questions, please feel free to ask. We welcome all people to our project. Our goal is to prove the Riesel Conjecture during the lifetime of Hans Riesel. To do that we need a lot of help. Hans Riesel was born in Stockholm, Sweden in 1929. According to his last email with me he is both healthy and very active in intellectual pursuits.

We have 82 values of k to find prime for. All that wish to help in our quest are truely welcome.

Lee Stephens
Riesel Sieve
www.rieselsieve.com

[jasong]

That was a wonderful explanation and I appreciate it. I'll probably never manage to remember that 6 digit number, but now I understand where it came from.

I appreciate your taking the time to explain it.

[jasong]

[double-post. Sorry :( ]