Mixed Sierpinksi problem

[tqft]

Woohoo.

Interesting.

http://seventeenorbust.com/ - read the front page news

[Death]

well can somebody explain how this can speed up SoB?

[Thommy3]

It can't.

[gopher_yarrowzoo]

It's already in use...
Just saying it "can't" doesn't exactly explain anything...

Now from what I've read of this very fine paper is that they basically caching as much as possible in to save the blasted bottlenecking you see sometimes which slows the whole process down. It is a finite balance getting this right.
I mean can you imagine it having to sit and calculate out k.2^n+1 everytime it needed to do work.... it does this once or rather I suspect rather nicely does a bit shift a big bitshift then does the work with the number cached it's a lot easier to work on small bits of the number that the whole thing at once as well thus the use of FFT with wieighted numbers since it's odd, that's half the numbers out and we do know a finite number of primes that it can be easily checked against. Also all the work from the mersenne project has helped bring down the amount of work done by the SoB program. Basically the more you can work out similtaniously the better as that means less time is taken. If we can prove one we are helping probably prove the other, number theorms are often like this with a few theorms supporting each other or acting as proof that if the number is for that theorm it's not for the other one..
Now I think I need to go lie down all this 2^n+/-1 log k is well :looney:
So there I think I may have just helped a little.

[Death]

thank you.

[philmoore]

well can somebody explain how this can speed up SoB?

As mentioned by gopher_yarrowzoo, the algorithm enhancements have already been benefitting SoB, as well as the Riesel investigation, for some time. When SoB eventually proves that 78557 is the smallest Sierpinski number, the weaker theorem proven in this paper will be superceded. My opinion is that the dual conjecture, that 78557 is also the smallest odd integer k such that k + 2^n is always composite, enhances the interest in the original Sierpinski problem. Hopefully, the fact that these two problems are related will increase the number of people willing to help investigate either problem. The dual problem will probably never generate as much interest as the original problem simply because its goal is the discovery of probable primes as opposed to provable primes, but the dual investigation being coordinated through the Mersenne Forum already seems to be getting a boost, particularly in the PRP-testing. (We are a little behind the optimal point in the sieving effort, but the project just started in October.)

[philmoore]

The dual Sierpinski search just found another probable prime this week. Details are at:
http://www.mersenneforum.org/forumdisplay.php?f=86

We named the project "Five or Bust" in homage to this great project, and have been fortunate enough now to eliminate two of the five remaining sequences. Our most recent success was of 2^n+28433, our lowest weight sequence - you may recall that 28433 was also one of the original k values for Seventeen or Bust as well.

[gopher_yarrowzoo]

The dual Sierpinski search just found another probable prime this week. Details are at:
http://www.mersenneforum.org/forumdisplay.php?f=86

We named the project "Five or Bust" in homage to this great project, and have been fortunate enough now to eliminate two of the five remaining sequences. Our most recent success was of 2^n+28433, our lowest weight sequence - you may recall that 28433 was also one of the original k values for Seventeen or Bust as well.

I like that "Five or Bust", shame you didn't decide to use "Five and Bust" - FAB :rock:

[Zuzu]

See http://www.mersenneforum.org/showthread.php?t=12376
[Tue Aug 25 08:20:40 2009]
UID: paleseptember/borg, 2^4583176+2131 is a probable prime! Wd1: E1C99FEE,00000000
Congrats to Ben Maloney and the whole group for this discovery, the first PRP found over 1M digits! :cheers:
This was for long, the lowest k without any PRP found for 2^n+k, as well as the lowest weight sequence for the three remaining k's. That improves the odds at finding a prime for all k's: for n below 5.2 x 10^8 at 50% probability and for n below 2.1 x 10^7 at 10% probability. Good luck! And maybe "two and bust" :rock:

[jjjjL]

See http://www.mersenneforum.org/showthread.php?t=12376
[Tue Aug 25 08:20:40 2009]
UID: paleseptember/borg, 2^4583176+2131 is a probable prime! Wd1: E1C99FEE,00000000
Congrats to Ben Maloney and the whole group for this discovery, the first PRP found over 1M digits! :cheers:
This was for long, the lowest k without any PRP found for 2^n+k, as well as the lowest weight sequence for the three remaining k's. That improves the odds at finding a prime for all k's: for n below 5.2 x 10^8 at 50% probability and for n below 2.1 x 10^7 at 10% probability. Good luck! And maybe "two and bust" :rock:

Wow! :D Exciting to see such progress with the dual project!

I also like seeing the new density graph with the two extra points beyond what we published less than a year ago!

Cheers,
Louie

[philmoore]

Thanks, it is gratifying to eliminate 3 of the 5 sequences in the first year of the project's existence. I don't expect the last 2 to be as easy, but who knows? Because the dual problem is related to the orignal Sierpinski problem, I hope that our progress may also help recruit more volunteers for Seventeen or Bust.

We have had two issues that I have been postponing, but must now start working on: sieving and double-checking. We are way undersieved (currently around 220T), but I had been hoping to eliminate a third sequence before ramping it up with a faster sieve file. Same with double-checking, not having to double-check 2131 will definitely save time and effort there. Perhaps we should move the sieving over to PrimeGrid, does anyone want to offer advice? In the meantime, if anyone wants to do manual sieving for a couple of weeks, we are currently eliminating 45 or so candidates for every 1T range. Zuzu has prompted me to take another look at my predictions, but I expect that there is still a good chance of having at least one sequence left by time we exhaust our current sieve file limit of 50 million, so I think we can do alot of sieving before we are wasting any effort.

I'm feeling lucky for Seventeen or Bust next, I'm predicting another prime before the end of 2009!

[paleseptember]

Where's the blush emoticon when you need it? :blush:

[philmoore]

I did not expect another prp to show up so quickly, but Engracio found 2^5146295+41693 the other day, only three months after our last one:
http://www.mersenneforum.org/showthread.php?t=12784
Four sequences down for the dual Sierpinski problem, one sequence to go! I tell you, though, statistically we expect the last one to be the toughest. Unless we get lucky, of course! I originally thought that we would be doing well to have 2 sequences left by the time we were near n=17M like Seventeen or Bust is now, but I'm not questioning success. Here's hoping for a bit of upcoming holiday luck for Seventeen or Bust now!

[enderak]

Awesome! :)

Was looking over the project's forum, and thinking I would start running a range or two later today.

Although, as a newcomer, I'd feel kind of guilty in the unlikely event I found the last sequence. Hopefully I can get a few fruitless ranges out of the way for you guys though. :)