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April 1st, 2014, 12:54 AM   #1
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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
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April 1st, 2014, 01:15 AM   #2
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The sequence generated is referred to as Central Polygonal Numbers.
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April 1st, 2014, 01:23 AM   #3
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please give me the details of natural distribution
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April 1st, 2014, 01:26 AM   #4
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Thanks Mark!

faysalelahikhan: What? You mean the distribution of the sequence or...?
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April 1st, 2014, 06:55 AM   #5
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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?)
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April 2nd, 2014, 01:37 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
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April 2nd, 2014, 05:31 AM   #7
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Quote:
Originally Posted by mathbalarka View Post
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 05:37 AM.
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