mersenneforum.org  

Go Back   mersenneforum.org > Other Stuff > Archived Projects > Prime Cullen Prime

 
 
Thread Tools
Old 2007-03-24, 15:44   #1
hhh
 
hhh's Avatar
 
Jun 2005

1011101012 Posts
Default 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:

Sieving with gcwsieve and the sieve.txt in the sieve reservation thread is going to be finished soon, but still available,

P-1 with prime95 or mprime can be reserved in the P-1 reservation thread and will advance as it becomes necessary, and

LLR, the actual prime hunting, with the LLR-client (not LLRnet); the content for the input files needs to be copy/pasted in the LLR-reservation thread.

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

Background:There are 14 Cullen primes 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 others 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.

Stats 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.

Last fiddled with by hhh on 2007-05-05 at 07:32
hhh is offline  
Old 2007-03-25, 05:59   #2
AntonVrba
 
AntonVrba's Avatar
 
Jun 2005

2·72 Posts
Default

Quote:
Originally Posted by hhh View Post
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.

HHH congratulation on your organisational skills and running with the idea that had started at http://primepuzzles.redgolpe.com/topic.asp?TOPIC_ID=10 . 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.
AntonVrba is offline  
Old 2007-05-05, 01:04   #3
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5·701 Posts
Default

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.
jasong is offline  
Old 2007-05-05, 07:42   #4
hhh
 
hhh's Avatar
 
Jun 2005

373 Posts
Default

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.
hhh is offline  
Old 2007-06-17, 00:18   #5
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5×701 Posts
Default

[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]

Last fiddled with by jasong on 2007-06-17 at 00:43
jasong is offline  
Old 2007-06-17, 00:53   #6
R. Gerbicz
 
R. Gerbicz's Avatar
 
"Robert Gerbicz"
Oct 2005
Hungary

101010100112 Posts
Default

Quote:
Originally Posted by hhh View Post
Background:There are 14 Cullen primes known, but only with composite exponents, and nobody knows if there is one with a prime exponent. That's why this project exists.
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.
R. Gerbicz is offline  
Old 2007-06-18, 01:06   #7
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5×701 Posts
Default

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?
jasong is offline  
Old 2007-06-18, 01:31   #8
Citrix
 
Citrix's Avatar
 
Jun 2003

1,553 Posts
Default

Quote:
Originally Posted by jasong View Post
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?
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.

Last fiddled with by Citrix on 2007-06-18 at 02:10
Citrix is offline  
 

Thread Tools


All times are UTC. The time now is 20:41.

Fri Jul 10 20:41:09 UTC 2020 up 107 days, 18:14, 1 user, load averages: 1.43, 1.66, 1.68

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.