20070324, 17:04  #1 
Sep 2002
Database er0rr
110010001010_{2} Posts 
Chance of sucess
Your project has only a few candidates after sieving over prime exponents. Have you considered your chances of success?

20070324, 17:57  #2 
Jun 2003
2×3×257 Posts 
Low but not zero. Just hoping if we are lucky.

20070324, 18:58  #3 
Jun 2005
373 Posts 
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. 
20070324, 19:10  #4 
Nov 2003
2·1,811 Posts 
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??

20070324, 19:20  #5 
Jun 2005
373 Posts 
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. 
20070324, 19:48  #6 
Nov 2003
2·1,811 Posts 
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): where 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 20070324 at 20:18 
20070326, 12:49  #7  
Aug 2006
Monza, Italy
5·7 Posts 
Quote:
then we have: 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 20070326 at 13:05 

20070426, 07:28  #8  
Sep 2002
Database er0rr
2·3·5·107 Posts 
Quote:
Quote:
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? 

20070426, 07:49  #9 
Jun 2003
2×3×257 Posts 
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. 
20070426, 08:02  #10 
Sep 2002
Database er0rr
2×3×5×107 Posts 
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 20070426 at 08:12 
20070426, 08:10  #11 
Jun 2003
2·3·257 Posts 
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. 
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