28 (number)
Template:For Template:Use mdy dates Template:Infobox number 28 (twenty-eight) is the natural number following 27 and preceding 29.
In mathematicsEdit
Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: <math>1+2+4+7+14=28</math>. As a perfect number, it is related to the Mersenne prime 7, since <math>2^{3-1}\times (2^{3}-1)=28</math>. The next perfect number is 496, the previous being 6.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Though perfect, 28 is not the aliquot sum of any other number other than itself; thus, it is not part of a multi-number aliquot sequence.
Twenty-eight is the sum of the totient function for the first nine integers.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Since the greatest prime factor of <math>28^{2}+1=785</math> is 157, which is more than 28 twice, 28 is a Størmer number.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Twenty-eight is a harmonic divisor number,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> a happy number,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> the 7th triangular number,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> a hexagonal number,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> a Leyland number of the second kind<ref>Template:Cite OEIS</ref> (<math>2^6-6^2</math>), and a centered nonagonal number.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
There are 28 convex uniform honeycombs.
Twenty-eight is the only positive integer that has a unique Kayles nim-value.
Twenty-eight is the only known number that can be expressed as a sum of the first positive integers (<math>1 + 2 + 3 + 4 + 5 + 6 + 7</math>), a sum of the first primes (<math>2 + 3 + 5 + 7 + 11</math>), and a sum of the first nonprimes (<math>1 + 4 + 6 + 8 + 9</math>), and it is unlikely that any other number has this property.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.Template:Citation needed
There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers.<ref>Template:Cite OEIS</ref>
Twenty-eight is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways: <math>5^2+1^2+1^2+1^2</math>, <math>4^2+2^2+2^2+2^2</math> or <math>3^2+3^2+3^2+1^2</math> (see image).<ref>A025368</ref><ref>A025359</ref>
In scienceEdit
- The fourth magic number in physics.
In other fieldsEdit
Twenty-eight is:
- Deriving from the 29.46 year period of Saturn's revolution around the Sun, the 28-year cycle as well as its subdivisions by 14 and 7 are supposed in astrology to mark significant turning points or sections in the course of a person's development in life. Thus, the number 28 has special significance in the culture of religious sects such as the Kadiri and the Mevlevi dervishes. The 28-beat metric pattern often used in the music compositions accompanying the main part of the Mevlevi sema ritual is called the "Devri kebir", meaning the "Big Circle" and is a reference to above astronomical facts about the year and the Saturn year.
- In Quebec, François Pérusse, in one of his best-selling Album du peuple made a parody of Wheel of Fortune in which all of the letters picked by the contestant were present 28 times. As a result, 28 became an almost mythical number used by many Quebec youths, the phrase "Y'en a 28" (There are 28 [Letters]) became a running gag still used and recognized more than 15 years later.
- Approximately the number of grams in an ounce, and used as such in the illegal drug trade.
ReferencesEdit
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External linksEdit
- Prime Curios! 28 from the Prime Pages