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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:

$d_{{1}}=p_{{2}}p_{{1}}=32=1$,

$d_{{10}}=p_{{11}}p_{{10}}=3129=2$,

$d_{{100}}=p_{{101}}p_{{100}}=547541=6$,

$d_{{1000}}=p_{{1001}}p_{{1000}}=79277919=8$,

$d_{{10000}}=p_{{10001}}p_{{10000}}=104743104729=14$ and so forth.
The first few values of $d_{{n}}$ for $n=1,2,3,\ldots$ are $1,2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,\ldots$ (OEIS A001223).
Keywords:
number theory, arithmetic function
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
11N05 no label found11A25 no label found11A41 no label found Forums
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new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier
new image: expected waiting time by robert_dodier
new image: plot W(t) = P(waiting time <= t) by robert_dodier
new question: Prove a formula is part of the Gentzen System by LadyAnne
Mar 30
new question: A problem about Euler's totient function by mbhatia
new problem: Problem: Show that phi(a^n1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia
new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz
Mar 26
new correction: Misspelled name by DavidSteinsaltz
Mar 21
new correction: underlinetypo by Filipe
Mar 19
new correction: cocycle pro cocyle by pahio
Mar 7
new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier
new image: expected waiting time by robert_dodier
new image: plot W(t) = P(waiting time <= t) by robert_dodier