prime difference function

The prime difference function is an arithmetic function for any positive integer $n$ , denoted as $d_{n}$ and gives the difference between two consecutive primes $p_{n}$ and $p_{n+1}$ :

$d_{n}\equiv p_{n+1}-p_{n}\;.$

For example:

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$d_{1}=p_{2}-p_{1}=3-2=1$ ,
•

$d_{10}=p_{11}-p_{10}=31-29=2$ ,
•

$d_{100}=p_{101}-p_{100}=547-541=6$ ,
•

$d_{1000}=p_{1001}-p_{1000}=7927-7919=8$ ,
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$d_{10000}=p_{10001}-p_{10000}=104743-104729=14$ and so forth.

The first few values of $d_{n}$ for $n=1,2,3,\ldots$ are $1,2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,\ldots$ (http://www.research.att.com/ njas/sequences/eisA.cgi?Anum=001223OEIS A001223).

Title	prime difference function
Canonical name	PrimeDifferenceFunction
Date of creation	2013-03-22 12:49:16
Last modified on	2013-03-22 12:49:16
Owner	XJamRastafire (349)
Last modified by	XJamRastafire (349)
Numerical id	6
Author	XJamRastafire (349)
Entry type	Definition
Classification	msc 11N05
Classification	msc 11A25
Classification	msc 11A41