mersenneforum.org  

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

 
 
Thread Tools
Old 2007-03-24, 17:04   #1
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

63218 Posts
Default Chance of sucess

Your project has only a few candidates after sieving over prime exponents. Have you considered your chances of success?
paulunderwood is online now  
Old 2007-03-24, 17:57   #2
Citrix
 
Citrix's Avatar
 
Jun 2003

155310 Posts
Default

Low but not zero. Just hoping if we are lucky.
Citrix is offline  
Old 2007-03-24, 18:58   #3
hhh
 
hhh's Avatar
 
Jun 2005

37310 Posts
Default

Somebody said he had calculated there were 0.27 primes out there up to 5M. Far from 0, I'd say. I like the idea of the possibility just to find one prime and to say mission accomplished (not in the George W. sense, of course).
H.
hhh is offline  
Old 2007-03-24, 19:10   #4
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2·1,811 Posts
Default

I already posted to the same effect, saying that considering n>1.4M and low weight it's very hard to find the next Cullen with any exponent but they deleted my post I wonder have I offended someone??
Kosmaj is offline  
Old 2007-03-24, 19:20   #5
hhh
 
hhh's Avatar
 
Jun 2005

17516 Posts
Default

I'm sorry, Kosmaj, when you posted, the subforum was a mess, (it is still, but less and less); I had to move threads, make new ones etc. (don't ask why), I tried to save your post, but then I physically deleted it, and it was gone; I apologize and I hope I didn't offend you from the very beginning.
Truly yours, H.
hhh is offline  
Old 2007-03-24, 19:48   #6
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2×1,811 Posts
Default

No problems, but when I posted there was only one thread ("Welcome") and one post in it.

FYI, it was proven back in 1976 that "almost all" Cullen numbers Cn are composite, i.e. (using cool TeX notation):
\lim_{x\to\infty}C_\pi(x)/x=0

where C_\pi(x) denotes the number of Cullen numbers Cn =< x which are prime. On the other hand it is "still conjectured that there are infinitely many Cullen primes but it is unknown if Cp can be prime for some prime p." (quoted from here where all currently known Cullen primes are listed.)

Last fiddled with by Kosmaj on 2007-03-24 at 20:18
Kosmaj is offline  
Old 2007-03-26, 12:49   #7
RedGolpe
 
RedGolpe's Avatar
 
Aug 2006
Monza, Italy

3510 Posts
Default

Quote:
Originally Posted by hhh View Post
Somebody said he had calculated there were 0.27 primes out there up to 5M.
If we assume that the chance of a random Cullen number n=k\cdot 2^k+1 to be prime is

\frac{2}{\log{n}}\approx \frac{2}{\log{k}+k\log{2}}

then we have:

\sum_{k=1.5M}^{5M}{\frac{2}{\log{k}+k\log{2}}}\approx 0.2344

where the sum is taken only on prime numbers. We also know that we don't have any result for k<1.5M.

Last fiddled with by RedGolpe on 2007-03-26 at 13:05
RedGolpe is offline  
Old 2007-04-26, 07:28   #8
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

63218 Posts
Default

Quote:
If we assume that the chance of a random Cullen number n=k\cdot 2^k+1 to be prime is

\frac{2}{\log{n}}\approx \frac{2}{\log{k}+k\log{2}}
I don't see this. Please explain why you use this assumption.

Quote:
then we have:

\sum_{k=1.5M}^{5M}{\frac{2}{\log{k}+k\log{2}}}\approx 0.2344

where the sum is taken only on prime numbers. We also know that we don't have any result for k<1.5M.
... is illogical.

If my chance of throwing a "six" is 1/6 then by throwing twice my chance does not become 1/3, but rather 1-(5/6)^2. That is the chance of being unsuccessful is 5/6 at the first throw and at the second throw it is (5/6)^2, meaning my chance of success at the second throw is 1-(5/6)^2 which is 11/36.

Am I missing something?
paulunderwood is online now  
Old 2007-04-26, 07:49   #9
Citrix
 
Citrix's Avatar
 
Jun 2003

1,553 Posts
Default

can we use the second graph here to predict the next prime

http://www.research.att.com/~njas/se...e?a=5849&fmt=5

It looks like the cullen prime numbers fall in a near straight line.
Citrix is offline  
Old 2007-04-26, 08:02   #10
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

17×193 Posts
Default

What is the plot of the prime k Cullen Primes?

What would be the projected size of the next (pure) Cullen and, with all things being equal, that the new prime would have a prime "k"?

Last fiddled with by paulunderwood on 2007-04-26 at 08:12
paulunderwood is online now  
Old 2007-04-26, 08:10   #11
Citrix
 
Citrix's Avatar
 
Jun 2003

1,553 Posts
Default

I tried to plot the log of the largest prime factor for all the prime cullen number's k and found the plot to be a straight line too.

May be the prime cullen prime is close by.
Citrix is offline  
 

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Chance of living N years? What's the formula for that? Stargate38 Lounge 19 2012-09-12 11:24
Percent chance of being prime henryzz Math 16 2007-11-11 16:21
Any chance of an NFSNET client for Intel Mac? fivemack NFSNET Discussion 1 2006-12-27 19:42
remote chance of a problem? nomadicus Software 13 2005-12-16 05:40
Chance to use modern Graphics Cards as.. Marco Hardware 28 2003-11-02 23:21

All times are UTC. The time now is 20:38.

Fri Jul 10 20:38:16 UTC 2020 up 107 days, 18:11, 1 user, load averages: 2.52, 1.91, 1.76

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.