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I am a little bit confused trying to name the compound fulvene:

fulvene

I'm not sure whether its name is 5-methylene-1,3-cyclopentadiene or 3-methylene-1,4-cyclopentadiene.

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Fulvene consists of a cyclopentadiene ring and a $\ce{{}=CH2}$ substituent group. According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the prefix ‘methylene’ is no longer recommended to designate the $\ce{{}=CH2}$ group. The preferred prefix is ‘methylidene’; thus, the systematic name of fulvene without locants is methylidenecyclopentadiene.

Concerning the numbering of locants, the current IUPAC recommendations read as follows.

P-14.4 NUMBERING

When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:

(…)

(e) saturation/unsaturation:

  (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;

  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);

(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;

(…)

Therefore, low locants are given first to the double bonds in the ring according to (e) and then to the prefix ‘methylidene’ according to (f). Thus, the correct systematic name is 5-methylidenecyclopenta-1,3-diene rather than 3-methylidenecyclopenta-1,4-diene since the locant set ‘1,3’ for the double bonds is lower than ‘1,4’.

35-methylidenecyclopenta-1,3-diene

Note that according to IUPAC nomenclature since 1993, locants are placed immediately before that part of the name to which they relate (e.g. cyclopenta-1,3-diene rather than 1,3-cyclopentadiene).

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    $\begingroup$ @hBy2Py - Retracted close vote. Note: This is something that gets sorted out in a Google search in one click of the button - the first hit is Wikipedia, the third is PubChem, the fourth is ChemSpider (the second is the Wikipedia entry for Fulvenes). If we're going to be a proxy for an internet search engine, we probably ought to discuss it in Meta. $\endgroup$ – Todd Minehardt Feb 18 '17 at 4:06
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    $\begingroup$ @ToddMinehardt You make a good point, but I feel all of the various nomenclature answers here add something that often is missing in resources like those resources you turned up in Google: explanation. Answerers here (Loong, often) typically go to considerable effort to explain why a given name fits the compound of the question. Much more valuable to the OPs and to future readers. $\endgroup$ – hBy2Py Feb 18 '17 at 4:39

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