# prime difference function

The 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:

• $d_{1}=p_{2}-p_{1}=3-2=1$,

• $d_{10}=p_{11}-p_{10}=31-29=2$,

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

• $d_{1000}=p_{1001}-p_{1000}=7927-7919=8$,

• $d_{10000}=p_{10001}-p_{10000}=104743-104729=14$ 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 PrimeDifferenceFunction 2013-03-22 12:49:16 2013-03-22 12:49:16 XJamRastafire (349) XJamRastafire (349) 6 XJamRastafire (349) Definition msc 11N05 msc 11A25 msc 11A41