20100907, 23:51  #1 
7·31·41 Posts 
Twin Prime Question
I'm interested in twins of the form k*2^n+/1.
One question: What is the probablity that there is a twin of that form with k<1M and n>1M? 
20100908, 02:38  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 

20100908, 02:59  #3  
Aug 2006
5987_{10} Posts 
Quote:
examples, right? Of course the constant factor needs work based on the residue classes 2^n takes on, as well as the factors in k. Edit: takes the factors of the kvalues into account. Last fiddled with by CRGreathouse on 20100908 at 03:04 Reason: make approximation clearer 

20100908, 05:04  #4 
2^{2}×23×37 Posts 
Where do the 21503 (second figure) and 4000 (first figure) numbers come from?

20100908, 13:00  #5  
Aug 2006
5,987 Posts 
Quote:
The other one is a calculated number based on the factorizations of k < 1000. Let me try for k < 1000000. OK, I get 14756135.8... Code:
sum(k=2,10^61,ff(k+k)^2,0.)/log(2)^2 Code:
4e6/log(2)^2*(zeta(2)sum(n=1,10^6,n^2,0.)) 14.75 (including factorizations) So with this larger range, the heuristic probability is high: with the Poisson model, it's something like 1  e^{14.75} = 99.99996% likely that such a pair of primes exist. 

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