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Message boards : Cullen/Woodall prime search : Prime Cullen Prime project

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JasonGoatcher

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Message 6757 - Posted: 28 Aug 2007 | 5:06:13 UTC

As most of you probably know, a Woodall prime is a prime of the form n*2^n-1 and a Cullen prime is a prime of the form n*2^n+1. What you might not know is there's a sub-project that deals with Cullen numbers, but only prime n. You see, while Woodall primes are known for both prime and composite exponents, with Cullen primes, there are no prime numbers known that could be assigned as n that would make n*2^n+1 prime. There's no reason to assume they don't exist, it's just that none are known.

I'm not sure what could be done, but I'm a little unhappy at the idea that if PrimeGrid takes over finding primes of the form n*2^n+/-1, that I'd possibly lose the ability to (1) choose Cullen or Woodall, and (2) if I chose Cullen, I might not be able to only do prime n numbers.

With Woodall numbers, it's no big deal, one or more Woodall's have already been found for both composite and prime ns. With prime Cullen numbers, a prime could be thought of as being like a rare gem. It might later fall to being the 1000th, millionth, or even billionth on the list of the largest known primes, but the first person to find a Cullen prime with a prime exponent will have that distinction forever, just like 2^127-1 will probably always have the distinction of being the biggest prime number found with pen and paper.

mdettweiler

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Message 6766 - Posted: 28 Aug 2007 | 15:37:35 UTC

I don't think that PrimeGrid in any way is "taking over" searching for certain types of primes; as far as I know, the Prime Cullen Prime project still exists and is running, and I don't think it has any connection at all to PrimeGrid.

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KEP

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Message 6768 - Posted: 28 Aug 2007 | 17:50:36 UTC - in response to Message 6766.

I don't think that PrimeGrid in any way is "taking over" searching for certain types of primes; as far as I know, the Prime Cullen Prime project still exists and is running, and I don't think it has any connection at all to PrimeGrid.

Well I'm not an admin, but greatly responsibel for Rytis first off supporting and running TPS through PrimeGrid. The TPS, Cullen and Woodall search aswell as any future searches, will all be subprojects, and the main project (which PrimeGrid is responsible off) will be PrimeGen. Of course the importance of the effort committed by the users of primegrid software, can never be underestimated. In fact if PrimeGrid continues to grow in popularity, not only they might be the first to ever find a 10 million digit primenumber, but eventually they will be the inhabitant of a no. 1 World Record Prime. Actually that would be another great reason to do a lot of sieving, since it will boost the big part of the Cullen and Woodall search :)

Hope it helped, else maybe Rytis can follow up :)

Regards and happy chrunching!

KEP

John
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Message 6797 - Posted: 2 Sep 2007 | 1:43:19 UTC - in response to Message 6757.

I'm not sure what could be done, but I'm a little unhappy at the idea that if PrimeGrid takes over finding primes of the form n*2^n+/-1, that I'd possibly lose the ability to (1) choose Cullen or Woodall, and (2) if I chose Cullen, I might not be able to only do prime n numbers.

Currently PG has ~27 times more candidates to test than PCP and is in the 2M range where PCP is in the 2.85M range. Therefore, that should allow some breathing room.

I encourage anyone who is interested in searching only for prime exponent Cullen primes (P*2^P+1) to please visit the Prime Cullen Prime forum.
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popandbob

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Message 6804 - Posted: 2 Sep 2007 | 23:05:57 UTC

Considering there is 2 projects why aren't we working together to save double testing everything?
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John
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Message 6807 - Posted: 3 Sep 2007 | 1:48:48 UTC - in response to Message 6804.

Considering there is 2 projects why aren't we working together to save double testing everything?

No work is being duplicated...well, technically it is. Since PCP is only doing a single pass, PG is double checking the results.
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John M. Johnson "Novex"
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Message 12736 - Posted: 14 Jan 2009 | 4:02:40 UTC

So as of now, with Cullens are we at a point where we are not just double checking? only 5 more WU's till 5M-6M is done for us, and with 6M-7M we have some to do so I'm curious where we stand as of late with Cullen's.
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John M. Johnson "Novex"

hhh

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Message 12742 - Posted: 14 Jan 2009 | 9:25:04 UTC

PG was in fact never merely doublechecking. The project called PrimeCullenPrime is dead for a long time. Basically, because PG was so much faster testing all candidates than PCP only the prime ones that there was no point in continuing.
PG is now, and has been prety much from the very beginning, doing firstpass and doublecheck tests.

[SG]Puzzle-Peter
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Message 13187 - Posted: 30 Jan 2009 | 18:57:27 UTC

Ta-raaaaaaa!

The 5M-6M range is complete! The last few WUs proved to be difficult with many compute errors, clients not responding etc. But at last every single one of 'em has been crunched down.

Congartulations, folks! Now for the next 1M range...
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There are only 10 kinds of people - those who understand binary and those who don't

John M. Johnson "Novex"
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Message 13197 - Posted: 30 Jan 2009 | 23:11:50 UTC - in response to Message 13187.

Ta-raaaaaaa!

The 5M-6M range is complete! The last few WUs proved to be difficult with many compute errors, clients not responding etc. But at last every single one of 'em has been crunched down.

Congartulations, folks! Now for the next 1M range...

Awesome!! Congratulations to everyone that crunched Cullen's, we did a great job getting them done. Now for the next 1m range hehe will be fun lets get us a prime!
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John M. Johnson "Novex"

[SG]Puzzle-Peter
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Message 13221 - Posted: 31 Jan 2009 | 17:43:09 UTC - in response to Message 13197.

[...] lets get us a prime!

That's exactly what I had in mind. We need a Cullen prime - let's do it!
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rogue
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Message 13236 - Posted: 1 Feb 2009 | 0:19:55 UTC

I found the last Cullen (base 2) prime in 2005. I'm surprised that none have been found since then because 5 Woodalls were found since then. There are about twice as many Woodalls as Cullens, so I would have expected 2 more before n = 6,000,000. Hopefully this project will be lucky enough to find one or two in the 6M-7M range.

Michael Goetz
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Message 74553 - Posted: 16 Mar 2014 | 12:27:22 UTC - in response to Message 13236.

I found the last Cullen (base 2) prime in 2005. I'm surprised that none have been found since then because 5 Woodalls were found since then. There are about twice as many Woodalls as Cullens, so I would have expected 2 more before n = 6,000,000. Hopefully this project will be lucky enough to find one or two in the 6M-7M range.

Yes, this thread is ancient, but I thought I'd point out just how incredibly prophetic Rogue was.

About two months later, April of 2009, we found 6328548*2^6328548+1, a 1.9 million digit mega prime. Then in August of 2009 we found 6679881*2^6679881+1, a 2 million digit mega prime. Both had exponents in the 6-7M range. Those two primes are currently #27 and #24 on the list of largest known primes.

No Cullens have been found since then. We're currently searching the 11-12M range.

The last Woodall, 3752948*2^3752948-1, is 1.1 million digits and was found in December of 2007. It's #56 on the list. That was the first mega prime ever found by PrimeGrid. We're currently searching Woodall numbers in the 12-13M range.
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Message boards : Cullen/Woodall prime search : Prime Cullen Prime project