April 18th, 2013, 05:54 AM  #21  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Splitting prime numbers in 2 sets Quote:
Dang, but you do nice work!  
April 18th, 2013, 06:41 AM  #22 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets
Thanks. Actually I tested the first 50,000 primes but discarded the kvalues, so I just regenerated the first thousand for you. 
April 18th, 2013, 01:26 PM  #23  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Splitting prime numbers in 2 sets Quote:
 
April 18th, 2013, 05:19 PM  #24 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets
There was a program to generate these numbers (not the kvalues, but that is easy enough to change) on the OEIS. I didn't use it though, it was too slow. So I wrote a faster version and submitted to the OEIS along with the first 10,000 values. Now maybe the next person who comes across this will be helped.

April 19th, 2013, 06:53 AM  #25 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets
Why : 18! mod 23 = 22 and 18! mod 29=28 23 and 29 are multiprimes. The same k make 2 multiprimes. Let us call t(k) the quantity of primes giving p1 as remains. t(1=2 Is t(k) finite or infinite? Is there a simple way to say that a prime number is multiprime or uniprime (some "belongity" test )? 
April 19th, 2013, 10:06 AM  #26  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets Quote:
Quote:
 
April 19th, 2013, 10:17 AM  #27  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets Quote:
I did not say that. I was talking about t(k) when n goes to infinite. That is different.  
April 19th, 2013, 10:26 AM  #28  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets Quote:
 
April 19th, 2013, 10:37 AM  #29  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Splitting prime numbers in 2 sets Quote:
 
April 19th, 2013, 11:45 AM  #30 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Splitting prime numbers in 2 sets
The limit does not exist. Probably and 

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