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-   Prime Cullen Prime (https://www.mersenneforum.org/forumdisplay.php?f=79)
-   -   Welcome! (https://www.mersenneforum.org/showthread.php?t=7618)

hhh 2007-03-24 15:44

Welcome!
 
This project is searching a Cullen prime, i.e. a prime of the form n*2^n+1, with prime exponent.

The project consists of three parts:

[B]Sieving[/B] with [URL="http://www.geocities.com/g_w_reynolds/gcwsieve/"]gcwsieve[/URL] and the sieve.txt in the [URL="http://www.mersenneforum.org/showthread.php?t=7616"]sieve reservation thread[/URL] is going to be finished soon, but still available,

[B]P-1[/B] with [URL="http://www.mersenne.org/gimps/"]prime95 or mprime [/URL] can be reserved in the [URL="http://www.mersenneforum.org/showthread.php?t=7615"]P-1 reservation thread[/URL] and will advance as it becomes necessary, and

[B]LLR[/B], the actual prime hunting, with the [URL="http://www.mersenne.org/gimps/"]LLR-client[/URL] (not LLRnet); the content for the input files needs to be copy/pasted in the [URL="http://www.mersenneforum.org/showthread.php?t=7614"]LLR-reservation thread[/URL].

Currently, there are about 4000 tests below 5M remaining, and any substantial help is appreciated to finish them off.

[B]Background[/B]:There are 14 [URL="http://primes.utm.edu/top20/page.php?id=6"]Cullen primes[/URL] known, but only with composite exponents, and nobody knows if there is one with a prime exponent. That's why this project exists.

The first stage of the project is the search in the range n=1.5M-5M. Below 1.5M, all Cullen numbers have been tested by [URL="http://www.prothsearch.net/cullen.html"]others[/URL] and no prime exponent yielded a prime(Doublecheck up to 400000). The range we are working on for the moment has been sieved by the same people up to 2.5 G, and with the improvements done by Citrix to Mark Rodenkirchs multisieve, and geoff's gcwsieve, based on Rodenkirch's code as well, currently being sieved beyond 3000G.

This project, given its small scale, is mostly run manually; reservations, database, all this is not automated and will probably never be. So, please don't expect realtime handling of the results etc, but the organisation should take place in reasonable delys, normally.

[B]Stats[/B] are not planned for the moment, but your reservations are going to be kept public in the reservation threads, so that one can figure out how much you contributed.

Finally, welcome again, and let us find that prime and finish the project soon.

Yours H.

AntonVrba 2007-03-25 05:59

[QUOTE=hhh;101990]This project is searching a Cullen prime, i.e. a prime of the form n*2^n+1, with prime exponent. There are Cullen primes known, but only with composite exponents, and nobody knows if there is such a prime. Well, we'll see.

... snip snip ....

Finally, welcome again, and let us find that prime and finish the project soon.

Yours H.[/QUOTE]


HHH congratulation on your organisational skills and running with the idea that had started at [URL="http://primepuzzles.redgolpe.com/topic.asp?TOPIC_ID=10"]http://primepuzzles.redgolpe.com/topic.asp?TOPIC_ID=10[/URL] . I wish this group luck and it will be great if the prime-Cullen-prime exponent can be found, there is no reason why it should not exist.

jasong 2007-05-05 01:04

Just out of curiousity, how many Cullen primes are known, and what are the chances that a prime Cullen prime hasn't been found because of simple dumb luck? In other words, if a number being searched is assumed to have the same odds of success as another number nearby in the range, what is the statistical chance that we would get this far without finding a prime Cullen prime.

hhh 2007-05-05 07:42

I put some of the information requested in the initial post. As for the chances of dumb luck, I don't know much; As for the Woodal-numbers, with -1 instead of +1, there exist prime exponents yielding a prime, e.g. 3, but that doesn't need necessarily something.

jasong 2007-06-17 00:18

[Off-topic]
Can't you just picture someone, later on in the main effort, where they don't care if the exponent is prime or not but they're only testing composites because they're at a lower n-value than this project.

(new person to the effort): I just noticed something remarkable about the sieved exponents, and I'm wondering if this has been recorded before. EVERY SINGLE n-value is composite. At the moment, I'm attempting to figure out why this is. Does anyone have any theories?

(Old hand in the project): That IS amazing. Keep at it, dude.

And meanwhile he's PMing everyone to check out this noob's post.
[/Off-topic]

R. Gerbicz 2007-06-17 00:53

[QUOTE=hhh;101990]
[B]Background[/B]:There are 14 [URL="http://primes.utm.edu/top20/page.php?id=6"]Cullen primes[/URL] known, but only with composite exponents, and nobody knows if there is one with a prime exponent. That's why this project exists.
[/QUOTE]

I think the probability that n*2^n+1 is prime for a random n number is O(1/n). This is also true for n=p prime numbers so the number of prime exponents Cullen primes up to exponent=n is sumprime(p=2,n,O(1/p))=O(log(log(n)). If this is true, than there're infinitely many Cullen primes with prime exponents. But the chance to find a slution is extremely small.

jasong 2007-06-18 01:06

I'm going to expose my ignorance here. Because the numbers are of the form

k*2^n+1,

and k is prime, does this not increase the chance that a number has a small factor like 3 or 5? I mean, with other k's there's an increased chance, an observable phenomenon, that one or more small primes are represented in the k-value. In my opinion, the fact that it's always a prime k decreases the chance that a random n-value will yield a prime.

Am I wrong?

Citrix 2007-06-18 01:31

[QUOTE=jasong;108448]I'm going to expose my ignorance here. Because the numbers are of the form

k*2^n+1,

and k is prime, does this not increase the chance that a number has a small factor like 3 or 5? I mean, with other k's there's an increased chance, an observable phenomenon, that one or more small primes are represented in the k-value. In my opinion, the fact that it's always a prime k decreases the chance that a random n-value will yield a prime.

Am I wrong?[/QUOTE]

Yes you are right. If we were only looking at numbers n==1 (mod 3) then there is an increased chance of finding a chance. A greater chance by 3/2 ie 1.5x more likely.

Using a program I calculated that if you sieve a bunch of numbers to 20M, then each candidate remaining is 30 times more likely to be prime compared to each before sieving.

edit: this is true in general, but if a series has special form of factors like mersenne numbers, then this is totally off. No one knows if prime cullen factors have a special form or not.


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