[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-563340-105":53,"doc-detail-563340-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","a-quick-look-at-prime-numbers-what-are-prime-numbers","A quick look at prime numbers - What are prime numbers?","","Prime numbers are positive natural numbers greater than 1 with exactly two positive divisors: 1 and the number itself. The text explains primality versus composite numbers, the Fundamental Theorem of Arithmetic, and why 1 is neither prime nor composite. It studies prime gaps using examples between 1 and 100, noting patterns such as mostly even gaps and listing known small gap sizes. It further discusses how many primes exist up to larger ranges and introduces the prime-counting function π(n) and its growth behavior.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/a-quick-look-at-prime-numbers-what-are-prime-numbers/563340/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/a-quick-look-at-prime-numbers-what-are-prime-numbers/563340.png","ImageObject",442,249,{"name":88,"@type":89},"Mabel","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-27","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":8},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What defines a prime number in this article?","Question",{"text":108,"@type":109},"A prime is a positive natural number greater than 1 that has exactly two positive divisors: 1 and the number itself. Numbers with other divisors are called composite.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Why is 1 not considered a prime?",{"text":113,"@type":109},"The article states that 1 has only a single positive divisor (itself). Since primes must have exactly two positive divisors, 1 is neither prime nor composite.",{"name":115,"@type":106,"acceptedAnswer":116},"How is the prime-counting function π(n) described?",{"text":117,"@type":109},"π(n) is the actual number of primes up to and including a given natural number. 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One possible reason for our fascination with prime numbers is that the inter-relationships between them and the patterns that they appear to create are so difficult to understand. Another possible reason is that the primes appear to exhibit both deterministic behaviours (i.e. fully determined on the basis of naturally-occurring relationships) and random behaviours (i.e. occurring by chance). Nobody has succeeded in creating mathematical models that predict the magnitudes of prime numbers exactly orthe numbers of prime numbers up to a given natural number. Other reasons for our fascination with primes may involve unexpected and quite exquisite relationships between prime numbers and certain mathematical functions and the seemingly disconnected islands of prime numbers, each surrounded by a sea of numbers that are not prime but which are related mysteriously to one another.  \nWhat are prime numbers?  \nPrimes are positive natural numbers, greater than 1, that have two positive divisors (i.e. have no divisors other than themselves and 1). Numbers that are not prime (i.e. have divisors other than themselves and 1) are known as composite numbers. The socalled Fundamental Theorem of Arithmetic tells us that every whole number greater than 1 is either prime or is a unique product of primes, apart from the order of multiplication. For example, 30 can be written as the product of three primes: 2 ×3 × 5. Figure 1 gives a table of the 25 prime numbers that lie between 1 and 100, in which the primes are shown against a shaded background.  \nBecause 1 has only a single positive divisor (itself), it is not a prime. In fact, because a composite number has more than one divisor, 1 is neither prime nor composite.  \nWe note that the gaps between these primes (which we define asthe difference between a given prime and the next prime) vary  \n*Correspondence: [david.lillis@nzis.ac. nz](david.lillis@nzis.ac. nz)  \nFigure 1: A table of the 25 prime numbers between 1 and 100.  \nconsiderably. We see from Figure 1 that, for numbers between 1 and 100, the gaps vary from 1 (i.e. the gap between 2 and 3) to 8 (that between 89 and 97). All prime gaps are even, apart from the first gap and, in fact, the first prime number (2) is the only even prime number.  \nThe first 15 gaps are as follows (compare with Figure 1):  \n1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4 and 6  \nHowever, though all prime gaps, except the first, are even natural numbers, many even natural numbers are not known prime gaps. Here are the fifteen smallest known gaps in ascending order:  \n1, 2, 4, 6, 8, 14, 18, 20, 22, 34, 36, 44, 52, 72 and 86.  \nWe see that the even natural numbers 10, 12, 16 and others within the range of this list are not known gap sizes. Thus, the known set of prime gaps is a subset of the even natural numbers.  \nDavid Lillis is the Senior Academic Manager (Research and Statistics) at the New Zealand Institute of Sport. Prior to joining NZIS, Dr Lillis was a senior statistician at the New Zealand Qualifications Authority. A former secondary school teacher David has also worked as a Senior Research Evaluator for the Foundation of Research, Science and Technology and has spent over 25 years in the research field.  \nDr Lillis is a past president of the New Zealand Association of Scientists.  \nHow numerous are the primes? Bernhard Riemann (1826 – 1866)  \nThere are 168 primes between 1 and 1000, 1229 primes between  \n1 and 10,000 and 78,498 of them between 1 and one million. We have tables of primes for much bigger natural numbers, but counting the primes becomes more and more difficult as we move along the number line to very large natural numbers.  \nAround 300 BC Euclid proved that there are infinitely many prime number","cbCaigcwClh15Cik","https://ap.wps.com/l/cbCaigcwClh15Cik","pdf",769274,6,"English","# Our fascination with the primes\n## What are prime numbers?\n## Prime gaps\n## How numerous are the primes?\n# Some Mathematical Expressions","[{\"question\":\"What defines a prime number in this article?\",\"answer\":\"A prime is a positive natural number greater than 1 that has exactly two positive divisors: 1 and the number itself. Numbers with other divisors are called composite.\"},{\"question\":\"Why is 1 not considered a prime?\",\"answer\":\"The article states that 1 has only a single positive divisor (itself). Since primes must have exactly two positive divisors, 1 is neither prime nor composite.\"},{\"question\":\"How is the prime-counting function π(n) described?\",\"answer\":\"π(n) is the actual number of primes up to and including a given natural number. The article notes values like π(1)=0, π(2)=1, and explains that primes make π(n) increase in steps with a tendency toward larger gaps at higher numbers.\"}]","A quick look at prime numbers - What are prime numbers? | PDF",1791829764]