April 19th, 2013, 11:22 AM  #31  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets Quote:
t(n) is not even known unless n reach some limit. How could you know that t(127) is equal to 3 at some stage t and could not increase to 4 or more at stage t+s ?  
April 19th, 2013, 11:36 AM  #32 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets
If it exist a prime number p < 127! but equal to (2k+1)p1 where k>0 then t(127) will increase by one. So you will not even know the value of t(k) until you reach the value of k! minus something. 
April 19th, 2013, 04:50 PM  #33 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets
Here is an example of t(10) You do not have 10 in your list above of k`s. But if we compute 10! mod 329891=329890 so t(10) will appear in the list and be equal to 1. 329891 is a certified prime (Wims) It is easy to find multiprimes starting from the factorial k. It will give you the definitive value of t(k) I`m sure that I will find another increment of t(10). 
April 19th, 2013, 04:59 PM  #34 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets
I did the test until 10!=3628600. Idid not find any other value so I`m sure that t(10)=1 (I hope I did not make mistakes). 
April 19th, 2013, 06:34 PM  #35  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets Quote:
Quote:
It's pretty clear that t(n) is finite. I could give you the proof but that would rob you of the ability to find it yourself (though if you insist...). I can prove that but I can't prove that this is infinite at the moment. The value of the lim inf is an open question for the time being.  
April 19th, 2013, 06:37 PM  #36  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets Quote:
 
April 19th, 2013, 07:07 PM  #37  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets Quote:
329891 I did not miss it. Read above. 329891 is a multiprime 11 is a uniprime. It seems to me that here is misunderstandings. See you tomorrow.  
April 19th, 2013, 07:21 PM  #38  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets
I don't see any such restriction in the definition of t: Quote:
 
April 20th, 2013, 04:33 AM  #39  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets Quote:
But I have to redefine t(k) because for uniprimes k should be = 0. It makes more sense. For the multiprimes k start from 1 to undefined value. Now there are some results to prove or at least to understand. The idea of splitting the set of prime numbers in 2 might lead to some unknown and maybe interesting territory or to somethng unuseful. I do not know.  
April 20th, 2013, 06:50 AM  #40 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets
Well, I suspect that the limit does not exist for this new function either, and that the limit inferior and limit superior are just like the original t(n).


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