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April 1st, 2014, 12:54 AM  #1 
Newbie Joined: Mar 2014 From: Slovakia Posts: 4 Thanks: 3  Interesting prime number sequence: (n^2)  (n1)
Hello, I've been looking into something and found this sequence that generates a lot of primes: X = (n^2)  (n1) X is a prime in a lot of cases. Is there a name for this sequence? I haven't found it so far. Sample primes: Thanks, David 
April 1st, 2014, 01:15 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs 
The sequence generated is referred to as Central Polygonal Numbers.

April 1st, 2014, 01:23 AM  #3 
Newbie Joined: Apr 2014 From: bangladesh Posts: 1 Thanks: 0 
please give me the details of natural distribution

April 1st, 2014, 01:26 AM  #4 
Newbie Joined: Mar 2014 From: Slovakia Posts: 4 Thanks: 3 
Thanks Mark! faysalelahikhan: What? You mean the distribution of the sequence or...? 
April 1st, 2014, 06:55 AM  #5 
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 
This is one of the entries on my list https://oeis.org/wiki/User:Charles_R...special_primes and is sequence https://oeis.org/A002383 in the OEIS. The number of primes of this form up to k is probably around $k\sqrt x/\log x$ with k between 2.2 and 2.3. This is covered by the HardyLittlewood Conjecture F though I'm not too sure of the actual constant here. (Anyone here good at computing infinite products of this type?) 
April 2nd, 2014, 01:37 AM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Quote:
 
April 2nd, 2014, 05:31 AM  #7 
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  I have code already written for Conjecture F, but this interval of D is suspect.
Last edited by CRGreathouse; April 2nd, 2014 at 05:37 AM. 

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