My Math Forum Interesting prime number sequence: (n^2) - (n-1)

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 March 31st, 2014, 11:54 PM #1 Newbie   Joined: Mar 2014 From: Slovakia Posts: 4 Thanks: 3 Interesting prime number sequence: (n^2) - (n-1) Hello, I've been looking into something and found this sequence that generates a lot of primes: X = (n^2) - (n-1) 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, 12:15 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs The sequence generated is referred to as Central Polygonal Numbers. Thanks from DavidGustafik
 April 1st, 2014, 12:23 AM #3 Newbie   Joined: Apr 2014 From: bangladesh Posts: 1 Thanks: 0 please give me the details of natural distribution
 April 1st, 2014, 12:26 AM #4 Newbie   Joined: Mar 2014 From: Slovakia Posts: 4 Thanks: 3 Thanks Mark! faysalelahikhan: What? You mean the distribution of the sequence or...? Thanks from MarkFL
 April 1st, 2014, 05:55 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 Hardy-Littlewood 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, 12:37 AM   #6
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Quote:
 Originally Posted by CRGreathouse (Anyone here good at computing infinite products of this type?)
I am not, thus I refrained from mentioning even the conjecture F, in case I have to compute that beast out

April 2nd, 2014, 04:31 AM   #7
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Quote:
 Originally Posted by mathbalarka I am not, thus I refrained from mentioning even the conjecture F, in case I have to compute that beast out
I have code already written for Conjecture F, but this interval of D is suspect.

Last edited by CRGreathouse; April 2nd, 2014 at 04:37 AM.

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