# [seqfan] Re: Differenes of conscutive primes

RGWv rgwv at rgwv.com
Fri Jan 14 02:20:27 CET 2011

```?Et al,

Using Harvey's Mmca, here are the powers of ten and the results. 10^7
finds all prime gaps from 1 through 99!

Bob.

1   0.000 sec  {1..4}
2   0.000 sec  {1..7, 9}
3   0.000 sec  {1..17}
4   0.015 sec  {1..32, 36}
5   0.234 sec  {1..50, 53, 56, 57}
6   3.744 sec  {1..77}
7  39.734 sec {1..99, 101, 102, 105, 110, 111}

-----Original Message-----
From: Harvey P. Dale
Sent: Thursday, January 13, 2011 5:27 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Differenes of conscutive primes

Richard is correct.  The following Mathematica program shows no
gaps from 1 through 69, and I'm fairly confident that expanding the
Range constant will fill in the missing numbers between 69 and 73:

Union[Rest[#/2&/@Differences[Prime[Range[500000]]]]]

Best,

Harvey

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Richard Mathar
Sent: Thursday, January 13, 2011 2:46 PM
To: seqfan at seqfan.eu
Subject: [seqfan] Re: Differenes of conscutive primes

http://list.seqfan.eu/pipermail/seqfan/2011-January/006863.html

vp> From seqfan-bounces at list.seqfan.eu Thu Jan 13 20:05:16 2011
vp> From: "Veikko Pohjola"
vp> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
vp>
vp> Consider the halved differences of consecutive primes
(Prime[k+1]-Prime[k])/2, k=2,3,4,.,K. Remove the duplicates and sort to
obtain an ordered set {1,2,3,.,a(i)}of all natural numbers from 1 to
a(i). The allowed numbers a(i) make up the following sequence: a(i) = 1,
2, 3, 4, 7, 17, 18,.
vp>
vp>

My impression from http://oeis.org/A000230 is that this sequence of
halved
prime gaps is dense, and does not miss numbers in the range 8 to 16.

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