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I am surprised that Mathworld Wolfram did not list "Arithmetic Derivative" but Wiki has

http://en.wikipedia.org/wiki/Arithmetic_derivative

You can use Arithmetic Derivative to formulate Goldbach's conjecture, twin prime and prime triples in an alternative way.

E. J. Barbeau, "Remark on an arithmetic derivative", Canad. Math. Bull. 4 (1961), 117 http://www.maa.org/mathland/mathtrek_03_22_04.html

Ufnarovski and Ã…hlander (2003) http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.pdf

Why didn't Weisstein's Mathworld mention arithmetic derivative at all?

@Benvitale

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4  
The main reason seems to be some form of the Occam razor... In plain English, that means that until you get some non-trivial result using your new notion/object/idea/whatever in an essential way, giving it a special name is not justified. –  fedja Jan 6 '12 at 23:17
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Have you tried asking Weisstein? –  Gerry Myerson Jan 7 '12 at 14:48
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I don't think Vitale deserved the brushoff that the moderators have given him. I certainly think the arithmatic derivative is an intriguing idea, and Vitale should have been encouraged to phrase his question in a more sensible fashion: such as has there been any interesting results shown/proved/reformulated. –  Mozibur Ullah Jan 25 '13 at 10:37
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closed as not a real question by Joël, Anthony Quas, fedja, Andreas Thom, Qiaochu Yuan Jan 6 '12 at 23:33

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