Note that Sierpinski problem is now almost resolved!!!

[Samidoost]

Congratulations to all the participants

That special multiplier k=28433 was THE ONLY k<78557 for which no probable prime of any of the forms k*2^n+1 and k+2^n was known:

4847+2^33
10223+2^19
19249+2^551542 (Probable prime)
21181+2^28
22699+2^26
24737+2^17
27653+2^39
33661+2^72
55459+2^17
67607+2^16389 (Probable prime)

Thus THE SIERPINSKI PROBLEM IS almost RESOLVED.
Great work!!!

-Payam:rotfl:

[Frodo42]

I don't totally understand this ... does the fact that these numbers have a prime mean that there is a bigger probability for a prime in the form K*2^n-1 ?

[Mystwalker]

Just what I wanted to ask. :)
Unfortunately, Google doesn't include symbols like + or * into the search, so it's difficult to find any k+2^n references.
Mathworld also doesn't mention this...

Does it have something to do with the covering set?

[ceselb]

afaik, it's proof that it will have a prime.

[olaright]

Help :help:

I am totally confused.

Ceselb, you use twice "it" in your answer, what does "it" mean? What question were you answering?

What does Samidoost mean?

Thanks Ola

[Joe O]

Start with k*2^n+1
If n is negative, show it as -m where m is positive.
k*2^(-m)+1
Multiply by 2^m
k*2^m*2^(-m)+1*2^m
Simplify
k*2^(m-m) +2^m
k*2^0+2^m
k+2^m

So Payam is talking about the negative extension, or negative form, of k*2^n+1.

[kugano]

I don't get it. If n is negative then k * 2^n + 1 is very likely not an integer. And that math is extremely dubious... you can't multiply the terms by 2^m because there's no "other side" of the equation to balance it out.

Payam is talking about the dual Sierpinski problem (http://sierpinski.insider.com/dual).

[vjs]

In laymans terms this is what they are talking about or perhaps I'm not getting what your talking about...

Also,

The other side is always equal to p.

If p has no factors (p') then it's prime, if p is not prime it has at least two factors where at least one p'<p^0.5 .


Now every k*2^n+1 will yeild a prime, guarented, if n can be negative or decimal.

Example make p=k*2^n+1 equal some prime , 3,5,7 etc by by using an non interger n or interger -m

set p=7 and use k=4847

7=(4847 x 2^n) + 1

6= 4847 x 2^n

6/4847 = 2^n

since you are now allowing n to be any value solve for n.

When you put n back into, k*2^n+1, you will always get a 7, a prime...

It's a joke since the n value doesn't fit the n's required to fit the proof, or am I missing something...

k.2n + 1 is composite for every n > 1

[vjs]

On another note, does anyone have comments on the following does this mean anything???

Of the remaining k's,

10223 is prime
19249 is prime
22699 is prime
27653 is prime
67607 is prime

But the others are not...
4847 (37 x 131) where 37 and 131 are both prime
21181 (59 x 359)
24737 (29 x 853)
33661 (41 x 821)
55459 (31 x 1789)


Of the primes found...

5359 (23 x 233)
28433 (prime)
44131 (prime)
46157 (101 x 457)
54767 (prime)
65567 (173 x 379)
69109 (prime)

[Joe O]

Originally posted by kugano
I don't get it. If n is negative then k * 2^n + 1 is very likely not an integer. And that math is extremely dubious... you can't multiply the terms by 2^m because there's no "other side" of the equation to balance it out.

Payam is talking about the dual Sierpinski problem (http://sierpinski.insider.com/dual).

Please read this post by Payam, (http://www.free-dc.org/forum/showthread.php?s=&postid=18200#post18200) where he states:


Originally posted by Samidoost
(2) dual Sierpinski problem , Which asks the same question for the sequence k+2^n, which could be considered as the negative continuation of the Proth sequence k*2^n+1:

k*2^(-n)+1=k/2^n+1=(k+2^n)/2^n

[Mystwalker]

On another note, does anyone have comments on the following does this mean anything???

Of the remaining k's,

10223 is prime
19249 is prime
22699 is prime
27653 is prime
67607 is prime

[...]

The only thing I know is that the upper 5 k's are also important for PSP... ;)

[Citrix]

Just an intresting note that the probability of finding a prime for a prime k or a non-prime k seems too be the same since the number of k's left that are prime are the same as the number of k's left that are non-prime.

Citrix
:cool: :cool: :cool:

[royanee]

Originally posted by Joe O
Please read this post by Payam, (http://www.free-dc.org/forum/showthread.php?s=&postid=18200#post18200) where he states:

In that post it says that Payam is actually talking about the 3rd Sierpinski problem, where you try to find a prime for k*2^n+1 or k+2^n. Of all the k's that need a prime, the union of the two sets' primes includes a prime for every k. If there's any more information regarding what this means to SoB, hopefully Payam can explain.

BTW: Citrix, where is PSP now, and how's that going?

[Citrix]

PSP is at www.mersenneforum.org, it is going well, but not any new primes recently. :(

15 k's left for which a prime needs to be found. we are at n=1.35 M and sieving around 60T, realy behind comapred to Sob.


Hope we could soon get some more users and find a prime. We are overdue for a prime.


Citrix
:cool: :cool: :cool:

[Jwb52z]

Originally posted by Citrix
PSP is at www.mersenneforum.org, it is going well, but not any new primes recently. :(

15 k's left for which a prime needs to be found. we are at n=1.35 M and sieving around 60T, realy behind comapred to Sob.


Hope we could soon get some more users and find a prime. We are overdue for a prime.


Citrix
:cool: :cool: :cool:

The main info page for PSP still says there are 21 candidates even though other places on the site say 15. There is only one main site, right? I mean I hope I am not looking at the wrong site about the project. The site I am talkinga bout is all in text and not much else with a white background.

[Samidoost]

Originally posted by royanee
If there's any more information regarding what this means to SoB, hopefully Payam can explain.


Although k*2^n+1 and k+2^n appear as 2 different things, they both are in fact parts of a single more general object.

Just like
-1, -2, -3, -4, -5, ...
which is the negative continuation of positive integers,

or like
1, -1, 2, -3, 5, -8, 13, -21, ...
which is the negative continuation of Fibonacci numbers,

the sequence k+2^n is THE negative continuation of k*2^n+1.


>>>>>> What does this mean to SOB? <<<<<<

It means that all the candidate sequences are IN FACT removed.

It means that THE Great Job is done.

It means that the recent prime will remain
THE MOST IMPORTANT prime found by SoB
EVEN IF LARGER PRIMES WILL BE FOUND.

It means that we are in a unique moment of the history of Sierpinski problem.

It means that the future primes are NOT important enough
to continue this way.

It means that it is the time for SoB to decide to reconfigure itself for more important objectives.

>>>>>>>> Suggestions <<<<<<<<<

If SoB wants to find the largest prime, there are very better places to search than these low weight proth sequences.

If SoB wants to find more important primes, there are very more important proths. Recalling the philosophy behind the proth numbers,
Q: Why proths are important?
A: ONLY BECAUSE they can divide Fermat numbers.

SoB CAN arrange for making 2005 a record year for Fermat divisors,
AT ABSOLUTELY NO COST.

Payam

[vjs]

I suppose this would also mean the end to PSP as well how about riesel?

What your suggesting is simply a continuation of prime searching at lower n...

Will there be an update here, http://sierpinski.insider.com

I'm also suprised, if the above is true, that we were simply not just searching 28433

[Samidoost]

PSP (Prime Sierpinski Search) is not affected by these considerations, since it is not bounded above by k=78557. Of course, it can focus on more important multipliers.

The Riesel search can be narrowed down to a very more limited count of k's as now is. So it may reach to such a historical point.

Even the positive Sierpinski search remains important, but not as important as many lower n goods waiting to be discovered.

You are right. It is the time for http://sierpinski.insider.com to be updated after almost 2 years. Let me do it in the next few days.

Payam

[Ken_g6[TA]]

There's still 19249 and 67607 to be proven. It might take longer to prove the primality of those k+2^n forms than it would to find a prime on the k*2^n+1 side. Especially for 19249.

I have a feeling we're going to keep searching on the positive side. But if you want to set up a project to look for these other Proth primes, here's the beginnings of an open-source server (http://www.mersenneforum.org/showthread.php?t=3498) you can use with the Seventeen or Bust client. Probably all you need is a database interface.

[vjs]

I think this is starting to become a poaching thread...

[Samidoost]

Thanks for the open source prp server.

But my objective is to redirect SoB's resources - which proves to be the best - to the best place.

For the k=19249 and k=67607, finding more probable primes seems simple, although it does not PROVE anything.

I hope that this thread will find its true place.
It depends on the particpants.

Perhaps a vote make help.

Payam

[kugano]

Payam, I don't understand your position. Are you saying that, for some fixed k, the existence of an n such that k + 2^n is prime implies the existence of an m such that k * 2^m + 1 is also prime? I've never heard anything like that, and I'm having a hard time convincing myself it could possibly be true. But if it is true, please provide a proof! It would indeed mean the Sierpinski problem is solved, provided the two probable primes could be proven.

[Citrix]

Originally posted by Jwb52z
The main info page for PSP still says there are 21 candidates even though other places on the site say 15. There is only one main site, right? I mean I hope I am not looking at the wrong site about the project. The site I am talkinga bout is all in text and not much else with a white background.


21 k's of which 15 PSP is working on and 6 SOB is working on. Of these 6 sob just found a prime. so only 20 k's are left. I just haven't updated the website yet.

Note:- PSP is a smaller problem than SOB since there are all odd under 78775 that SOB is considering where as PSP is only intested in prime k's under 265711. So when we reach the level SOB is at there will be fewer k's left for PSP compared to SOB.

Citrix
:cool: :cool: :cool:

[mike74]

Originally posted by kugano
Are you saying that, for some fixed k, the existence of an n such that k + 2^n is prime implies the existence of an m such that k * 2^m + 1 is also prime?

I don't know the answer but I think another way to ask this would be: if k = a - 2^n where a is prime, is there an m such that 2^m * (a - 2^n) + 1 is prime?

I think this could be disproved if a Sierpinski number could be written as b - 2^j where b is prime. Or it could be proved if it is proven that Sierpinksi numbers can never be written this way.

[Mystwalker]

Originally posted by Ken_g6[TA]
There's still 19249 and 67607 to be proven. It might take longer to prove the primality of those k+2^n forms than it would to find a prime on the k*2^n+1 side. Especially for 19249.

It seems like it's not such a big problem to prove 67607+2^16389 prime. I looked around and found out that general primalty proving programs already proved a number with 7760 digits.
Currently, I'm testing out Primo (http://www.ellipsa.net/) - does someone knows of a better program for this purpose?

There is also a multiprocessor program, which resently proved a 15,071 digits prime ( http://www.ellipsa.net/primo/record.html ), but unfortunately, this one seems not to be public. :(

[vjs]

Has anyone tried factoring either of these "primes" ?

Also if this is true but those 2 values are not prime etc, it would still mean that we only have to test 2 k values... if they are prime we could always do similar numbers of the k/n type to search for a n=34M prime for example.

We could also chose a k=3 or some small number and simply start at some high n, (I think k=2 is already taken...) I believe small k are faster with the new program, this way the user base wouldn't be lost nor team competion etc. The good old "End phase one" trick of DC

[Citrix]

You could use Miller rabins test.

[Citrix]

Here is a way to proove what everyone is saying

Let there be a covering set for a SOB's k then for all n, k*2^n+1 has a factor.
The let the numbers of this covering set be indicated by set f with members f1, f2 etc. note f1, f2 .... are all the lowest prime factors.

So 2^f-1% f is 0 for all members of the set.

Now I will try to show that if there is a covering set for K*2^n+1 then there is a covering set for K+2^N. The vice-versa can also be prooved.

So,

K*2^n+1 is divisible by f
K*2^n+1%f =0
multiplying both sides by 2^f-1-n
K*2^f-1+2^f-1-n%f
K+2^f-1-n

Hence all n in K*2^n+1 correspond to a K+2^N.

This will be more clear by taking a sierpinski number and seeing that it has the same covering set.

So if it can be shown that k+2^n has no covering set for a given k then k is not a seirpinski number. There are 2 ways to show that a given k does not have a covering set

1) find a prime for that k
2) It could be that K+2^n=a, a is prime, a is part of the covering set for K*2^n+1.


If either of the 2 are false then the k is a sierpinski number.


So it can be K+2^n method can be applied to SOB, but it cannot be prooved that the PRP is found is a part of the covering set, so this method is almost useless. But since it is unlikely that it is a part of covering set so this method does indicate that none of the k's are sierpinski numbers.


I am sure the above is really confusing, but I don't have a easier way of explaining it.


Citrix



:cool: :cool: :cool:

[kugano]

You could use Miller rabins test.
Miller-Rabin isn't a proof.

[kugano]

K*2^n+1 is divisible by f
K*2^n+1%f =0
multiplying both sides by 2^f-1-n
K*2^f-1+2^f-1-n%f
K+2^f-1-n
That algebra is completely bogus! Let's all just calm down and let Payam himself explain what he's talking about.

[Citrix]

Originally posted by kugano
That algebra is completely bogus! Let's all just calm down and let Payam himself explain what he's talking about.

proove it is bogus before stating some thing.:swear:

[vjs]

K*2^n+1 is divisible by f
K*2^n+1%f =0


% is suppose to represent

K*2^n+1 = K*2^n+1%f = 0
------
f


WHAT!!!

Sure, K*2^n+1 is divisible by f and whenever f is a factor (or prime) will equal some interger, but not zero.

K*2^n+1 = mf (where m = 1,2,3,...)

multiplying both sides by 2^f-1-n now this f is the same f as the orignal f

O.K ... lets just work the LHS since we may disagree on the RHS

I'd have to say

(K*2^n+1)(2^f-1-n) =
produces
k*2^(n+1+f-1-n) =
now
k*2^f =

Sorry I just can't get this to work...

Agreed prove its bogus where am I wrong as well?

[Citrix]

%=mod
YOu know what mod is

[Mystwalker]

Guys, let's all calm down, ok? No :bonk: , please.

I don't think that any harsh words have to be spoken/written here. It's all about math - even in that part where it's possible to proof everything. :)
So I'm pretty sure that there's no problem in either proving or disproving all the ideas/assumptions/whatsoever mentioned here.


Originally posted by Citrix
So 2^f-1% f is 0 for all members of the set.

While trying to comprehend your formula, I stumbled about this one.
What is the definition for 2^f, as f is a set?

[kugano]

Sorry, I'm not trying to flame anyone. But your "simplification" simply doesn't work out... try it again, being very careful to properly observe the rules of algebra, and I'm sure you'll get it. Also, thinking of "mod" as an operation is a common misunderstanding, especially among programmers who are used to the % operator in most languages. The word "mod" is just a way of indicating that you're using modular arithmetic rather than the set of all integers. The proper way to say "4 % 3 = 1" is "4 == 1 (mod 3)." The LHS is "4," not "4 % 3," and the RHS is "1." I think this LHS/RHS confusion might be the source of some of the algebra problems.

Anyway, I would feel a lot better if we could just let Payam himself explain. I think he's the most capable person out of anyone here to show us the light. Second-guessing each other isn't going to turn up anything productive. Thanks!

[vjs]

My God Citrix,

Especially when you earlier said...


I am sure the above is really confusing, but I don't have a easier way of explaining it.

I'm not a math guru, if you meant MOD say MOD not %, I have seen people use % for division instead of /, yes it's wrong.

I was actually trying to work through your post before
That algebra is completely bogus! was made. When I made my post so please don't take mine to offend. Also you have to realise where your posting and what your saying and :swear: from an outsider is :spank: worthy :D

Also I'm also trying to figure out what this means for our team etc. I was trying to understand what you were saying about finding primes of k's etc. Perhaps you could explain covering sets better...

Also can the case be made that, k= 60451 and 75353 in the form k+2^n need to find primes before the problem is solved. Correct me if I'm wrong here...

Does that mean that if we find a prime for k=60451 and 75353 in the k*2^n+1 form we don't need to do k+2^n, no.

It might be faster to search these k's and form true, but it may also be faster for us to finish our 10 k prove our primes and claim a few more records in the process?

[vjs]

Either way would it mean that we would only want to continue testing for non-prime k's...

[royanee]

Originally posted by Citrix

K*2^n+1 is divisible by f
K*2^n+1%f =0
multiplying both sides by 2^f-1-n
K*2^f-1+2^f-1-n%f
K+2^f-1-n


Ok, if we include the parentheses, this seems to make sense to me.

K*2^n+1 is divisible by f
K*2^n+1 (mod f) = 0
Multiply both sides by 2^(f-1-n)
K*2^n*2^(f-1-n) + 1*2^(f-1-n) (mod f) = 0
K*2^(n+f-1-n) + 2^(f-1-n) (mod f) = 0
K*2^(f-1) + 2^(f-1-n) (mod f) = 0 , f-1-n will now be replace by N which is some other value of n
K*2^(f-1) + 2^N (mod f) = 0

Now, to get to K + 2^N (mod f) = 0, 2^(f-1) (mod f) must = 0. As the factors f can only be prime, then 2^(p-1) = 0 (mod p). I can only assume that this is known to be true if that is how it was simplified. I know it works for 3, 5, 7, so I'll assume this for now. Note: I know that 2 doesn't work, but we never use 2 as part of the covering set, so we don't care. Also, using 2 for K doesn't work because 2 * 2^n = 2^(n+1), and then we're just working with mersenne like numbers (I forgot what the 2^n+1 numbers are called).

So K*1 + 2^N (mod f) = 0, and thus K + 2^N = 0 (mod f)

End? Hopefully I understood that correctly. I am interested in that covering set thing, it would be nice to prove that a prime exists even if we don't know what it is equal to.

[mike74]

Originally posted by royanee
As the factors f can only be prime, then 2^(p-1) = 0 (mod p).

You mean 2^(p-1) = 1 (mod p).

[Joe O]

Originally posted by royanee
2^(f-1) (mod f) must = 0. As the factors f can only be prime, then 2^(p-1) = 0 (mod p). I can only assume that this is known to be true if that is how it was simplified. I know it works for 3, 5, 7, so I'll assume this for now. Fermat's Little Theorem (http://mathworld.wolfram.com/FermatsLittleTheorem.html)

[Joe O]

Originally posted by Mystwalker

While trying to comprehend your formula, I stumbled about this one.
What is the definition for 2^f, as f is a set?

I think he means 2^fi where fi is a member of the set f.

[Samidoost]

Originally posted by kugano
Payam, I don't understand your position. Are you saying that, for some fixed k, the existence of an n such that k + 2^n is prime implies the existence of an m such that k * 2^m + 1 is also prime?
The correct answer is: Not necessarily.

Unfortunately, we cannot deduce any useful SCIENTIFIC statement for SoB.
The main Sierpinski problem is still remained unsolved with 10 candidates remained to decide. And the dual considerations adds no new SCIENTIFIC information on them. In fact SoB is doing its job remarkably Great. So

>>>>>>>>>>>> What is my position <<<<<<<<<<<<

The information provided by dual considerations is totally PHILOSOPHICAL for SoB, not SCIENTIFIC. It provides a great PHILOSOPHICAL justification to put SoB aparatus working on more useful objectives.

Continuing the SoB with the main Sierpinski problem is not a SCIENTIFIC mistake. It is a PHILOSOPHICAL mistake.

Note that from now on, the PHILOSOPHY does not support SoB.

kugano (David): you are one of the main owners of SoB.
Please consider my suggestions.
Please vote.

Payam

[vjs]

So is the other side of your "PHILOSOPHICAL" suggestion that primes do infact exist for our remaining k? Basically this is what I have understood from the above.

... means is that the problem is "solved" but not proven ...

To put this another way, we now know for certain that eventually we will find a prime for each k b/c one exisits, where before we did not know for certain that each k had a prime...

If this is the case, I definetly vote in favor of continuing since no matter how high n gets we will eventually find a prime for each k, I'm sure other feel the same.

Also any prime is useful, so it would still be scientifically useful to know the lowest n producing a prime for each k in the K*2^n+1 form.

[kugano]

Payam, I see what you're saying about scientific utility. I have two responses to that. Firstly, how useful is any number theory-related distributed computing project? I'll grant you that I'm not a professional mathematician (never went beyond a B.S. in math), but I really can't think of any concrete way in which any of these projects are improving the world. We're finding big primes, cool... but what does it matter? The primes we discover have no practical uses whatsoever, at least not that I know about.

Number theory (and mathematics in general) is clearly extremely important. Extending our theoretical knowledge of mathematical constructs gives us better and better tools we can use to help understand and relate to the physical world. But neither SB nor any other projects I'm aware of have produced, or will ever produce, any new theoretical results. In a sense, we're just cleaning up after the theorists. Someone proves that 78,557 is a Sierpinski number, and wham, guys like us come along behind him and start crunching 1 thru 78,556 to prove it. We're not turning out any theorems, we're just combining those theorems with what we're good at -- computer technology -- to do something fun.

The second response is that, even if the Sierpinski problem were really important and useful, it would not be the reason SB is cool. The reason SB is cool, and IMHO the reason any distributed computing project is cool, is that we have the power of a massive supercomputer and we've paid (and been paid) precisely zero New Turkish Liras for it. That is our success. It's nice that we've also found a few primes along the way, but when it comes down to it, SB is only really cool as a process and as an example of how a couple of hobbyists with some spare time can put together a serious heavy-duty crunching network.

Now, putting all that aside... if someone can show us a problem that actually does have legitimate real-world value, one that's suitable for a distributed computing approach, of course we'd consider it! I'm not particularly attached to this problem, for the very reasons mentioned above. I would like to finish it, and I don't want to give up, but if someone makes a solid argument in favor of switching and if the user community agrees, well, that's fine! Doesn't matter what problem we're working on. We'll still be a cool project and we'll still be successful.

[kugano]

Whoops, I didn't mean to cut everyone out in that post. I should have said, "what a couple of hobbyists with some spare time -- and several thousand people willing to participate -- can accomplish." Mike, Louie and I wouldn't have got very far using just our own machines!

[royanee]

Originally posted by mike74
You mean 2^(p-1) = 1 (mod p).

hehe, yeah! That's what I meant to write. At least that's the only mistake I made (in typing it back up and not in understanding it). Also, so that's Fermat's Little Theorum? *does a little dance* :elephant:

I still want to find some more primes! :)

[vjs]

:blush: Yes I know I know, I wish the math specific to this project was explained a little better. I just recently started to understand what p :eek: was. Imagine how abstact this is to non-math gurus, when people don't understand p and how it's used in sieving. Now how does one try to explain factoring or ecm ... what it does sure, but how it works :confused: .

I'd also like to congradulate and thank Kungao for stepping up and posting in other threads as well. "Laying all the cards on the table so to speak"

Perhaps someone can create a few pages describing sieve, P-1, prp, and more the more advanced math on the main page.

I find myself trying to explain sieve on our team forum every other week. I'm sure the majority of the text is written in this forum, by myself at ARS, and various other places. If someone were so inclinded they could knock it out with links and pictures in a matter of a few hours.

Lets hope for continued success in the furture and thank everyone for their efforts thus far.

:hifi:

[kugano]

Indeed that would be an excellent way to contribute to the project. Eventually it'd be cool if we had a whole set of pages on seventeenorbust.com explaining the math, like GIMPS but maybe more detailed.

I'd be happy to help review / clarify the math (as much as I can, anyway, given that really I'm only an amateur myself when it comes to the real number theory behind everything) if someone wanted to work on this.

[Vato]

I'm still trying to decode what Samidoost meant in his last post (without any algebra). This is obviously an important thread, and I'm troubled that I don't understand any of it, despite previously thinking I vaguely knew what we were doing (as a layman). Whenever it reaches its conclusion, I'd appreciate a selection of simple translations that might help me out :confused:

[kugano]

My suggestion is: don't kill yourself trying to understand this thread. There is (with all due respect) a lot of misinformation and second-guessing here, and the issues have been clubbed to death. The important points as I see them are:

1 - The "combined problem" -- finding a prime, for each k < 78,557, in either of the sequences k * 2^n + 1 or k + 2^n -- is now essentially solved. I say "essentially" because for two of the multipliers, only pseudoprimes are known; they haven't been proven prime with a deterministic test.

2 - In Payam's opinion, solving the original "Sierpinski problem" (only considering the sequence k * 2^n + 1) is no longer important, because of Point 1. In his opinion we should now be spending our CPU cycles on more useful problems.

3 - In my opinion, Payam is only half correct -- the Sierpinski problem is not that important, and it never was. SB is just as cool today as it was a month ago. Could we make the world a better place for our children by working on a different problem instead? Maybe. But until someone can suggest a plausible alternative, I don't see why we can't just be happy that we are the second most productive prime-finding operation of all time, that it was done for free, and that we all have had a hell of a lot of fun doing it!

[Vato]

Amen to that - especially point 3.

I reckon we should complete all 17 as was originally intended, including the checking that it is the lowest n for that k which is prime. After that, who knows? PSP and Riesel seem the closest relations, but that needn't be the criteria. I suspect it's a long way to go yet.

[Samidoost]

Originally posted by vjs
So is the other side of your "PHILOSOPHICAL" suggestion that primes do in fact exist for our remaining k?

The answer is: NOT NECESSARILLY

This is the beautiful part of the problem: Even for the most prime rich proth sequences found, we does not know that there will exist another prime or not.

Currently we know the answer ONLY for Sierpinski and Saridis numbers.

Payam

[zwilnik]

Originally posted by kugano
My suggestion is: don't kill yourself trying to understand this thread. There is (with all due respect) a lot of misinformation and second-guessing here, and the issues have been clubbed to death. The important points as I see them are:

1 - The "combined problem" -- finding a prime, for each k < 78,557, in either of the sequences k * 2^n + 1 or k + 2^n -- is now essentially solved. I say "essentially" because for two of the multipliers, only pseudoprimes are known; they haven't been proven prime with a deterministic test.


Why hasn't someone proved the pseudoprimes prime or not yet? I'm sure that someone with a more powerful computer than mine, would be glad to help.

If the person with the table that has predected the previous primes is correct we will find the next two ore three primes in the next five years or so. But the last two will take over a thousand years to be found. I guess the only thing known about them is they will be found in December. :rotfl:

[kugano]

Why hasn't someone proved the pseudoprimes prime or not yet? I'm sure that someone with a more powerful computer than mine, would be glad to help.
Because they're huge, and there's no efficient test for numbers of that form. Proth's theorem gives us an extremely fast way to test numbers for SB (relatively speaking), but it only works on numbers of the form k * 2^n + 1. Testing a 500,000-bit number using a general-purpose test is currently impossible with today's computer technology. (It would probably be better to say "intractable" than "impossible.")


If the person with the table that has predected the previous primes is correct we will find the next two ore three primes in the next five years or so. But the last two will take over a thousand years to be found. I guess the only thing known about them is they will be found in December. :rotfl:
Maybe, but there are a few other factors to keep in mind. Computing power grows exponentially with time. In five years we'll have much faster machines to test with. Also, one would hope that in five years we'll have a lot more users than we do now. George is cranking out frequent improvements to the PRP core. And it's just possible the next five years might see an algorithmic improvement -- someone may find a more efficient test than Proth's theorem. True, eventually we may get stuck anyway... but let's not give up just yet!

[Keroberts1]

its also true that these numbers are from a formula that gets less reliable as the numbers get bigger. if a prime is found for 67607 then the final estimate could drop considerably.

[mackerel]

Originally posted by kugano
3 - In my opinion, Payam is only half correct -- the Sierpinski problem is not that important, and it never was. SB is just as cool today as it was a month ago. Could we make the world a better place for our children by working on a different problem instead? Maybe. But until someone can suggest a plausible alternative, I don't see why we can't just be happy that we are the second most productive prime-finding operation of all time, that it was done for free, and that we all have had a hell of a lot of fun doing it!
If people want to do a project with more visible benefit to the world, there are plenty of others distributed computing projects out there to choose from. No one is forced to do SB. I can and do jump around the various projects myself. For now I'm doing SB because of what it is, and I hope to see it completed some time.

[Keroberts1]

to what project are you refering? I hope not distributed folding or genome at home. Frmo what I've hear dall oftheir work is estimated by expert biologists to be bull and to have no chance of ever benefitting anyone. Then there is seti at home. Great if you want ot help the scientist at berkely map out the galaxy not at finding aliens though( they aren't even trying to find aliens). They are just using that as a ploy to get membership. Even if there is a alien signal out there its not likely Setiathome will findit because they only search a single type of signal and what are the chances that it happens ot be the one aliens would use. So i would like ot know what roject yo uwere refering to. I chose SB because it is fun, the people here are nice, ti has an eventual end, and because as a user we get ot participate, make reckomendations, perhaps even help out. Try going to distributed.com wiht a reckomendation see how far that goes. BTW all of the encryptions being attemped on all of the DC projects trying to break encryptions have not been used for years. no DC project is going ot break any currently used encryptions.

[vjs]

I think Keroberts1 post is a little less hostile than it come across, everything he has said is true in my opinion. I've participated in ALOT of projects, let me first start put by telling everyone here some unwritten rules we use at ARS.

1. All questions are worth asking and answering by anyone who chooses to post.

2. Projects can be critized and commented upon, but no one's effort should ever be critized unless they NEGATIVELY impact a project.

3. It's your computer and time do with it as you choose.

With that being said Yes I do have opinions....

Seti, I was a big supporter untill I found out about the cheating and the actual Hydrogen drift effort of the project. Also they don't listen to their users, the project is heavily under optimized intentionally to reduce project output.

As for the biological projects? What do you expect... computer guys doing biology, good work perhaps but the community will frown. Protein folding, thisis good and highly adaptable to computers, but it's an idea, it's been proven not sure how well it works... Besides you always have to compare to crystal data, Raman, NMR, gels, etc.

As for the encryption projects they are good and fun, but can be proven on paper by one guy with a little stats in a weekend. Put three guru's a stats, computer, code breaker, together for diner and they can figure out hold long it would take to complete before desert. Code breaking projects are very similar to finding primes BUT the answer has some importance with primes. Primes are primes the hidden message doesn't need any meaning nor does it have one, knowing primes will help encryption.

As for Sob, I think it's great and currently at a point were it's still fun, practical, an alternative to gimps. Most importantly great people and moderators creaters that listen and actually comment and participate.

Now how many project out there have you seen the moderators/creators actively participate with the users?? For this particular project you don't have to go far.

^
|
|


Indeed that would be an excellent way to contribute to the project. Eventually it'd be cool if we had a whole set of pages on seventeenorbust.com explaining the math, like GIMPS but maybe more detailed.

I'd be happy to help review / clarify the math (as much as I can, anyway, given that really I'm only an amateur myself when it comes to the real number theory behind everything) if someone wanted to work on this.

Who the heck is this "kugano" guy anyways???

[ceselb]

Originally posted by vjs Now how many project out there have you seen the moderators/creators actively participate with the users?? For this particular project you don't have to go far.[/B]

Just to be clear, I was a "normal user" before becoming a mod (admins weren't around back then, so I stepped up to maintain the coordination threads).

[mackerel]

Originally posted by Keroberts1
to what project are you refering? [snip]
I take it that was in reply to my previous post? My main point was only that if anyone doesn't think SB is sufficiently worthwhile, they don't have to do it and can go find something else to do with their CPU cycles. Personally I'd like to see SB continue to the end, whenever that may be.

[kugano]

Who the heck is this "kugano" guy anyways???
Er, what?

[vjs]

Trying to make a point about project creators/co-authors participating in discussion forums... :thumbs:

[mike74]

I think that in the absence of proof that k + 2^m can be prime implies that k * 2^n + 1 must be prime for some n, the question of whether any k < 78,557 exists for which k * 2^n + 1 is never prime is completely open and that this project should continue at least until such a proof is made.

[Citrix]

Originally posted by vjs
I think Keroberts1 post is a little less hostile than it come across, everything he has said is true in my opinion. I've participated in ALOT of projects, let me first start put by telling everyone here some unwritten rules we use at ARS.

1. All questions are worth asking and answering by anyone who chooses to post.

2. Projects can be critized and commented upon, but no one's effort should ever be critized unless they NEGATIVELY impact a project.

3. It's your computer and time do with it as you choose.

With that being said Yes I do have opinions....

Seti, I was a big supporter untill I found out about the cheating and the actual Hydrogen drift effort of the project. Also they don't listen to their users, the project is heavily under optimized intentionally to reduce project output.

As for the biological projects? What do you expect... computer guys doing biology, good work perhaps but the community will frown. Protein folding, thisis good and highly adaptable to computers, but it's an idea, it's been proven not sure how well it works... Besides you always have to compare to crystal data, Raman, NMR, gels, etc.

As for the encryption projects they are good and fun, but can be proven on paper by one guy with a little stats in a weekend. Put three guru's a stats, computer, code breaker, together for diner and they can figure out hold long it would take to complete before desert. Code breaking projects are very similar to finding primes BUT the answer has some importance with primes. Primes are primes the hidden message doesn't need any meaning nor does it have one, knowing primes will help encryption.

As for Sob, I think it's great and currently at a point were it's still fun, practical, an alternative to gimps. Most importantly great people and moderators creaters that listen and actually comment and participate.

Now how many project out there have you seen the moderators/creators actively participate with the users?? For this particular project you don't have to go far.

^
|
|



Who the heck is this "kugano" guy anyways???


I couldn't agree more with you. Being a biologist, I know that the biological DC projects are just crap. Calculate all the money people who are running these clients would pay as electrical bill for running the DC project. If this money was given a lab to do research I am sure that they can come up wiht better and faster results.


Citrix
:cool: :cool: :cool:

[Jwb52z]

Citrix, how could they all be crap? I mean, they do it faster than a lab could process things and it uses coding done by scientists and people who understand science. For example, the Find a Drug project found sveral candidates for cancer inhibitors last year that a lab is now doing trials with in real life.

[vjs]

I wouldn't go as far as calling them junk, folding molecular interactions etc... It's all van der waals forces, bond geometry, orbital overlap, electron crowding, attraction replusion, and summing up energy, making sure a step doesn't break a bond irrereversibly, all at the same time, etc etc etc. It's all physics and chemisty ... once the program is setup it can be done by computer easily.

But I wonder how many factors are left out, limits, etc. This is where the critics step in...

I've never looked deeply into find a drug, but I know there is a database program out there for organic chemistry. Basically it's a database of all known chemical reactions synthetic steps etc.

Basically you put in what you have and what you want. The program will suggest possibilites, but it's still upto the person to decide what to do. This would be a very dumbed down verison of find a drug from what I understand. I'd just like to know how many suggestions by the project could have worked but were thrown out by the researcher.

Regardless, do which ever project makes you happy. I personally like projects that can't get funding, after all ... are we not donating our time.

[Ken_g6[TA]]

Originally posted by Samidoost
Currently we know the answer ONLY for Sierpinski and Saridis numbers.

PayamOkay, I know what a Sierpinski number (http://primes.utm.edu/glossary/page.php/SierpinskiNumber.html) is, but what's a Saridis number? Mathworld doesn't have it, and Google gets me only one hit (http://primes.utm.edu/curios/page.php?number_id=834).

P.S. A simple sieve link (http://primes.utm.edu/glossary/page.php/SieveOfEratosthenes.html) and PRP link (http://primes.utm.edu/glossary/page.php?sort=PRP) to add to your FAQ if someone makes one. I'd sure like a better explanation of sieving over n's.

[kugano]

Presumably named after Pavlos Saridis (http://primes.utm.edu/bios/page.php?id=188), but that's as much as I know...

[jjjjL]

Another prime another rant from Payam about how we need to switch to Fermat divisors cause he likes them.

Anyone else remember Payam doing this before? I know I do:
VINTAGE PAYAM circa December 2002 http://www.free-dc.org/forum/showthread.php?s=&threadid=2069

That was when he started complaining after prime #2.

He's done it after just about every prime find. Last time he started spouting off about how SB *HAD* to switch to suit his needs. He basically posed as a project admin / SB spiritual leader and started telling users we were going to start switching soon. I deleted his posts, he called me a fascist, he pissed and moaned.... so I proved him right by fascistly deleting his new trolling thread about what a fascist I was.

Payam - We appreciate your advice and early support for SB but you need to realize that your proposals are totally contrary to our project. Please respect our wishes to continue working on our own terms.

Cheers,
Louie

[Samidoost]

Here is the starting link for Pavlos Saridis' numbers:
http://groups.yahoo.com/group/primenumbers/message/8479

Waclaw Sierpinski have discovered (around the 1950s) an 18 digit k for which there could not exist a prime in k*2^n+1, by finding this covering set of primes
{3,5,17,257,65537,641,6700417}
Later Hans Riesel (around the 1990s) have found k=78557.

Pavlos Saridis (in 2002) have found a new series of k's for which there are not primes in k*2^n+1. For the multipliers introduced by him the covering process is partially done by factorization. They are Sierpinski numbers for which a finit covering is not found (and is not likely to be found).

In literature, each k for which there is no primes (for any reason) in k*2^n+1 is called a Sierpinski number. So Saridis numbers are in fact a special case of Sierpinski numbers.

2002 was a very good year for Sierpinski problem:
(computational) SoB was borned!
(theoritical) Saridis numbers was introduced by Pavlos
(philosophical) dual proths was re-introduced by me!

Payam :)

[Samidoost]

Originally posted by jjjjL
Another prime another rant from Payam about how we need to switch to Fermat divisors cause he likes them.

Anyone else remember Payam doing this before? I know I do:
VINTAGE PAYAM circa December 2002 http://www.free-dc.org/forum/showthread.php?s=&threadid=2069

That was when he started complaining after prime #2.

He's done it after just about every prime find. Last time he started spouting off about how SB *HAD* to switch to suit his needs. He basically posed as a project admin / SB spiritual leader and started telling users we were going to start switching soon. I deleted his posts, he called me a fascist, he pissed and moaned.... so I proved him right by fascistly deleting his new trolling thread about what a fascist I was.

Payam - We appreciate your advice and early support for SB but you need to realize that your proposals are totally contrary to our project. Please respect our wishes to continue working on our own terms.

Cheers,
Louie

I had never called you a fascist.
Moreover I have always supported SOB.
AND I AM SUPPORTING IT JUST NOW.

I am just suggesting to do something more fruitful.
And this is not a harm for SoB. It is a service.

I have always suggested the best for SoB. Because I thought (and think) that it deserves it. My proposals ARE NOT BY ANY MEANS contrary to SoB.

I am not an enemy. I am a real friend.
I had never called you a fascist.

Payam :cry:

[Keroberts1]

comparatively to setiathome we have a very small amount of resources. Currently they claim to have around 70 teraflops of power in their network. Ours claims 33.64 but i believe that is highly exagerated because of the properties of the cem/s units.
My user stats page reports me having around 7.5 times as much power as i actually have on my P4. This means we have a little over 4 teraflops available to us. Ok. So where am i going with this. If we had the resources of setiathome we could have done all of the work we've done to date in less than a month. Remember if we had our current resources and algorithims we could have gone from zero to current in less than 300 days. Kinda makes setiathome look like its resources are being wasted since nothing but publicity is ever created by its programs. Not to mention the users are disreguarded and the stats are rittled with fraud. To bad we can't steal a few of those users away and bring them somewhere their participation would be much more appreciated.

[vjs]

I will second Keroberts1 opinions once again. There was a link posted sometime back showing some wu's processed 11 times!!! I think all units should be processed twice, 3 is fine, and perhaps a 4th were there are errors but more than 4 ????

Regardless I think the idea of seti is a great one socially, search "The Drake Equation" great for math/stats guys. To have >1M people actually sign up shows something, if one want's complain about no aliens etc, etc, it's generaly pretty easy to stop that arguement with the comment. "There is more scientific/statistical evidence showing the possibility of ET than God using the drake equation".

The most conservative estimates possible for the drake equation show at least one civilization, earth (13 for battlestar fans :D ). The standard predicition last time I checked was something like 5,000-50,000 planatary civilizations at current time in various stages of development. Which sounds like alot but would mean or closest neighbour would be over ??50 light years away?? due to the portion of the galaxy we are in.

With that being said sounds like we need a lounge thread.

[zwilnik]

Originally posted by Keroberts1
comparatively to setiathome we have a very small amount of resources. Currently they claim to have around 70 teraflops of power in their network. Ours claims 33.64 but i believe that is highly exagerated because of the properties of the cem/s units.
My user stats page reports me having around 7.5 times as much power as i actually have on my P4. This means we have a little over 4 teraflops available to us. Ok. So where am i going with this. If we had the resources of setiathome we could have done all of the work we've done to date in less than a month. Remember if we had our current resources and algorithims we could have gone from zero to current in less than 300 days. Kinda makes setiathome look like its resources are being wasted since nothing but publicity is ever created by its programs. Not to mention the users are disreguarded and the stats are rittled with fraud. To bad we can't steal a few of those users away and bring them somewhere their participation would be much more appreciated.

I found DC's because of SetiAtHome. While running SETI, I wondered if there was something better out there and found Sob. I tried Sob, decided to finish my one hundred SETI WU's. Then I came back here. The only thing SETI about me now is my team name. :|party|:

SetiAtHome is good for getting your foot in the door for DC projects. Too bad we can't advertise on SetiAtHome and get some more people. :cheers:

[philmoore]

Just a quick correction - John Selfridge in 1962 was the person who first identified 78557 as a Sierpinski number and conjectured that it was the smallest.

I, for one, would welcome a distributed project looking for large Fermat number divisors, but I would not like to see this project abandoned. OR BUST means what it says! I would at least like to see a couple more primes found so that SoB can say it has made it at least "halfway" towards its goal.

[Samidoost]

Phil:
Thanks for correction.
I had not access to my notes at the moment, I had relied on my memory.

SoB:
I will not discuss more on the subject. I have made my alert.
Best wishes for SoB

Payam :gangpunch

[engracio]

Payam:


I will not discuss more on the subject. I have made my alert.

Is that mean you won't bring this subject again about we going in the wrong direction etc, etc.:)

I've been on situations deep in a forest thinking I was lost like a mofo, alas turns out I was on the correct trail all along.:scared:

Somebody might think, ohh what a waste of resources/assets. Too bad its my resources/assets. Luckily here in the mid-west of America, we still have the right to do what we damn please with what we we own. :blush:

Got to go, got a prime to hunt down. Be seeing u next time around.:)



e:)


http://www.clanhosts.com/dev/sobsig/sig.php?engracio

[Samidoost]

Originally posted by engracio
Payam:
Is that mean you won't bring this subject again about we going in the wrong direction etc, etc.:)

Yes, exactly.:thumbs:

But remember:
YOU HAVE ALREADY FOUND THE IMPORTANT PRIME.
NEXT PRIMES WILL NOT BE AS IMPORTANT AS THIS ONE.

Best wishes again for SoB
Payam :)

[Keroberts1]

I thought you were done








ohh wait ... wait ...










wait....










ok now i think he's done





whew...










see ya after the next prime.