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The Product Types Ontology: Class Definition for "Prime number"

This page is part of http://www.productontology.org/, a huge, precise dictionary of product types and brand names for marking up Web sites with schema.org or the GoodRelations e-commerce standard.

Breaking news: schema.org has just implemented our proposal to define an additionalType property with the use of this service in mind!

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http://www.productontology.org/

On this page: Usage(schema.org/Microdata, RDFa, Facebook) Contact Information Caching Policy License Acknowledgments References

pto:Prime_number (rdf:type owl:Class)

URI http://www.productontology.org/id/Prime_number
rdfs:subClassOf gr:ProductOrService, http://schema.org/Product
rdfs:label Prime number (as a class or brand name of products of services)
Translation(s):  Priemgetal@af;  Primzahl@als;  Numero primero@an;  Frumtæl@ang;  عدد أولي@ar;  عدد اولى@arz;  মৌলিক সংখ্যা@as;  Númberu primu@ast;  Sadə ədəd@az;  Pėrmėnis skaitlios@bat-smg; 

rdfs:comment

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or involve 5 itself. However, 6 is composite because it is the product of two numbers that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt{n}. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. the largest known prime number has 24,862,048 decimal digits. There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm. Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals. (Source: Wikipedia, the free encyclopedia, see http://en.wikipedia.org/wiki/Prime_number)

Note: The extraction of the abstract from the Wikipedia page may sometimes yield imperfect results. We are improving the algorithm regularly.

is rdfs:domain of gr:category gr:color gr:condition gr:depth gr:hasEAN_UCC-13 gr:hasGTIN-14 gr:hasMPN gr:hasManufacturer gr:hasStockKeepingUnit gr:height gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo gr:weight gr:width
is rdfs:range of gr:includes gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo

Note: This is a generic list. Some of the properties may not be applicable to this particular type of object.

Trademark Disclaimer:  Since this service returns class descriptions for potentiall any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. We assume no liability for the absence of trademark rights and other damages. See the section "License" below for details.

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Usage

The following shows how to model that you offer to sell [a/an/some] Prime number for $ 19.99.

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Microdata / Use with http://schema.org/Product

One of the most powerful usages of the class definitions from this site is to describe the type of your page and product for the schema.org product markup in Microdata syntax much more precisely.

Simply add the full URI of a class from this site, e.g. http://www.productontology.org/id/Prime_number as an additional type as follows:

<div itemscope itemtype="http://schema.org/Product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Prime_number" />
    <!-- other schema.org properties go in here -->
</div>		

Note: In HTML5, it is valid to use the <link> element in the body of a HTML document.

Here is a complete example:

<!DOCTYPE html>
<html>
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Prime_number</title>
</head>
<body>
<div itemscope itemtype="http://schema.org/Product" itemid="#product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Prime_number" />
    <span itemprop="name">.. a short name for the object ...</span>
    Product description: 
    <span itemprop="description">... a longer description ...</span>
    <div itemprop="offers" itemscope itemtype="http://schema.org/Offer" itemid="#offer">
        <span itemprop="price">$19.99</span> 
        <link itemprop="availability" href="http://schema.org/InStock" />In stock
    </div>
</div>
</body>
</html>

Turtle Syntax

@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix pto: <http://www.productontology.org/id/> .
@prefix gr: <http://purl.org/goodrelations/v1#> .
@prefix foo: <http://example.com/> .

# The object
foo:myObject a <http://www.productontology.org/id/Prime_number> ;
	a gr:SomeItems ;
	gr:name "... a short name for the object ..."@en ;
	gr:description "... a longer description ..."@en .

# The agent (person or company) who is offering it
foo:ACMECorp a gr:BusinessEntity ;
	gr:legalName "ACME Corp" ;
	gr:offers foo:Offer .
		
# The offer to sell it
foo:Offer a gr:Offering ;
	gr:includes foo:myObject;
	foaf:page <http://URI_of_the_page_containing_the_offer.com>;
	gr:hasBusinessFunction gr:Sell ;
	gr:validFrom "2011-01-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:hasPriceSpecification
         [ a gr:UnitPriceSpecification ;
           gr:hasCurrency "USD"^^xsd:string ;
           gr:hasCurrencyValue "19.99"^^xsd:float ;
           gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ] .

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDFa

<!DOCTYPE html>
<html version="HTML+RDFa 1.1" xmlns="http://www.w3.org/1999/xhtml">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Prime_number</title>
</head>
<body>
<div xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:foaf="http://xmlns.com/foaf/0.1/"
     xmlns:gr="http://purl.org/goodrelations/v1#"
     xmlns:pto="http://www.productontology.org/id/"
     xmlns:foo="http://example.com/"
     xmlns:xsd="http://www.w3.org/2001/XMLSchema#">

<!-- The agent (person or company) who is offering it -->
   <div about="#ACMECorp" typeof="gr:BusinessEntity">
      <div property="gr:legalName">ACME Corp</div>
      <div rel="gr:offers">
<!-- The offer to sell it -->	
         <div about="#offer" typeof="gr:Offering">
            <div rel="gr:hasBusinessFunction" resource="http://purl.org/goodrelations/v1#Sell"></div>
            <div rel="gr:includes">
<!-- The object -->	
               <div about="#myObject" typeof="http://www.productontology.org/id/Prime_number">
                  <div rel="rdf:type" resource="http://purl.org/goodrelations/v1#SomeItems"></div>
                  <div property="gr:description" xml:lang="en">... a longer description ...</div>
                  <div property="gr:name" xml:lang="en">.. a short name for the object ...</div>
               </div>
            </div>
            <div rel="foaf:page" resource="http://URI_of_the_page_containing_the_offer"></div>
            <div rel="gr:hasPriceSpecification">
               <div typeof="gr:UnitPriceSpecification">
                  <div property="gr:hasCurrency" content="USD" datatype="xsd:string">$ </div>
                  <div property="gr:hasCurrencyValue" datatype="xsd:float">19.99</div>
                  <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00" 
					   datatype="xsd:dateTime"></div>
               </div>
            </div>
            <div property="gr:validFrom" content="2011-01-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
            <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
         </div>
      </div>
   </div>
</div>
</body>
</html>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDF/XML

<?xml version="1.0" encoding="UTF-8" ?>
<rdf:RDF xmlns:gr="http://purl.org/goodrelations/v1#" 
  xmlns:pto="http://www.productontology.org/id/" 
  xmlns:xsd="http://www.w3.org/2001/XMLSchema#" 
  xmlns:foaf="http://xmlns.com/foaf/0.1/" 
  xmlns:foo="http://example.com/" 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<!-- The object -->
  <rdf:Description rdf:about="http://example.com/myObject">
    <rdf:type rdf:resource="http://www.productontology.org/id/Prime_number"/>    
    <rdf:type rdf:resource="http://purl.org/goodrelations/v1#SomeItems"/>
    <gr:name xml:lang="en">... a short name for the object ...</gr:name>
    <gr:description xml:lang="en">... a longer description ...</gr:description>
  </rdf:Description>
<!-- The agent (person or company) who is offering it -->
  <gr:BusinessEntity rdf:about="http://example.com/ACMECorp">
    <gr:legalName>ACME Corp</gr:legalName>
    <gr:offers rdf:resource="http://example.com/Offer" />
  </gr:BusinessEntity>
<!-- The offer to sell it -->   
  <gr:Offering rdf:about="http://example.com/Offer">
    <gr:includes rdf:resource="http://example.com/myObject" />
    <foaf:page rdf:resource="http://URI_of_the_page_containing_the_offer"/>
    <gr:hasBusinessFunction rdf:resource="http://purl.org/goodrelations/v1#Sell"/>
    <gr:validFrom rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-01-24T00:00:00+01:00</gr:validFrom>
    <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-12-24T00:00:00+01:00</gr:validThrough>
    <gr:hasPriceSpecification>
      <gr:UnitPriceSpecification>
        <gr:hasCurrency rdf:datatype="http://www.w3.org/2001/XMLSchema#string">USD</gr:hasCurrency>
        <gr:hasCurrencyValue rdf:datatype="http://www.w3.org/2001/XMLSchema#float">19.99</gr:hasCurrencyValue>
        <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
          2011-12-24T00:00:00+01:00</gr:validThrough>
      </gr:UnitPriceSpecification>
    </gr:hasPriceSpecification>
  </gr:Offering>

</rdf:RDF>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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SPARQL Query

prefix foaf: <http://xmlns.com/foaf/0.1/> 
prefix xsd: <http://www.w3.org/2001/XMLSchema#> 
prefix pto: <http://www.productontology.org/id/> 
prefix gr: <http://purl.org/goodrelations/v1#> 
prefix foo: <http://example.com/> 

# Find the cheapest offer for a Prime_number

SELECT * WHERE{
?company gr:offers ?offer .
?offer a gr:Offering .
?offer gr:hasBusinessFunction gr:Sell .
OPTIONAL {?offer rdfs:label ?label } .
OPTIONAL {?offer gr:name ?label } .
OPTIONAL {?offer rdfs:comment ?label } .
OPTIONAL {?offer gr:description ?label } .
?offer gr:hasPriceSpecification ?p .
?p a gr:UnitPriceSpecification .
?p gr:hasCurrency ?currency .
?p gr:hasCurrencyValue ?price .
?offer gr:includes ?product .
?product a <http://www.productontology.org/id/Prime_number> .
}
ORDER BY (?price)
LIMIT 10

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Facebook Open Graph Protocol

You can also use the class definitions from this site for better describing the type of your page or product for the Facebook Open Graph Protocol.

Simply define the namespace prefix pto: in the <html> element of your page

<html version="HTML+RDFa 1.1" 
	xmlns="http://www.w3.org/1999/xhtml" 
	xmlns:pto="http://www.productontology.org/id/" 
	>

and use the compact URI (CURIE) pto:Prime_number in combination with og:type as follows:

	<meta property="og:type" content="pto:Prime_number"/>

A complete example is here.

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Contact Information

Univ.-Prof. Dr. Martin Hepp

E-Business and Web Science Research Group
Chair of General Management and E-Business
Universität der Bundeswehr München
Werner-Heisenberg-Weg 39
D-85579 Neubiberg, Germany

Phone: +49 89 6004-4217
eMail: mhepp(at)computer.org (preferred mode of communication)
Web: http://www.heppnetz.de/
Web: http://www.unibw.de/ebusiness/

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Caching Policy

In order to minimize the load on the Wikipedia API, all requests are cached internally for 72 hours. This means that changes to the English Wikipedia will be available in this service within 72 hours or less if the same entry has been requested before. Classes not requested within the last six hours are always guaranteed to be in sync with the latest version in Wikipedia.

The RDF/XML dump file is updated every 12 hours only.

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License

The class definition text is taken from Wikipedia, the free encyclopedia under a Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license. Accordingly, the ontology class definitions are available under the very same license.

Trademark Disclaimer:  Since this service returns class descriptions for potentially any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. If you want us to block a certain name, please send your request including proof of your rights on the name to our contact address listed below.. Any of the trademarks, service marks, collective marks, design rights or similar rights that are mentioned, used, or cited in this service are the property of their respective owners. Their use here does not imply that you may use them for any purpose other than for the same or a similar informational use as contemplated by the original authors of the underlying Wikipedia articles under the CC-BY-SA and GFDL licensing schemes. Productontology.org is neither endorsed by nor affiliated with any of the holders of any such rights and as such cannot grant any rights to use any otherwise protected materials. Your use of any such or similar incorporeal property is at your own risk.

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Acknowledgements

Thanks to Stefano Bertolo, Julien Chaumond, Bob Ferris, Kingsley Idehen, Axel Polleres, Andreas Radinger, Alex Stolz, and Giovanni Tummarello for very valuable feedback, and to Katharina Siorpaes and Daniel Bachlechner, who contributed to the initial analysis of the stability of Wikipedia URIs back in 2007.

The work on The Product Types Ontology has been supported by the German Federal Ministry of Research (BMBF) by a grant under the KMU Innovativ program as part of the Intelligent Match project (FKZ 01IS10022B).

BMBF logo

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References

Wikipedia: Prime number, available at http://en.wikipedia.org/wiki/Prime_number.

Hepp, Martin: GoodRelations: An Ontology for Describing Products and Services Offers on the Web, Proceedings of the 16th International Conference on Knowledge Engineering and Knowledge Management (EKAW2008), Acitrezza, Italy, September 29 - October 3, 2008, Springer LNCS, Vol 5268, pp. 332-347.

Hepp, Martin; Siorpaes, Katharina; Bachlechner, Daniel: Harvesting Wiki Consensus: Using Wikipedia Entries as Vocabulary for Knowledge Management, IEEE Internet Computing, Vol. 11, No. 5, pp. 54-65, Sept-Oct 2007.

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