28 (number)

28 (twenty-eight) is the natural number following 27 and preceding 29.

In mathematics

Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: $1+2+4+7+14=28$. As a perfect number, it is related to the Mersenne prime 7, since $2^\times (2^-1)=28$. The next perfect number is 496, the previous being 6.

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.

Since the greatest prime factor of $28^+1=785$ is 157, which is more than 28 twice, 28 is a Størmer number.

Twenty-eight is a harmonic divisor number, a happy number, the 7th triangular number, a hexagonal number, a Leyland number of the second kind ($2^6-6^2$), and a centered nonagonal number.

It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).

It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...

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 ($1 + 2 + 3 + 4 + 5 + 6 + 7$), a sum of the first primes ($2 + 3 + 5 + 7 + 11$), and a sum of the first nonprimes ($1 + 4 + 6 + 8 + 9$), and it is unlikely that any other number has this property.

There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.

There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers.

Twenty-eight is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways: $5^2+1^2+1^2+1^2$, $4^2+2^2+2^2+2^2$ or $3^2+3^2+3^2+1^2$ (see image).

In science

* The fourth magic number in physics.

In other fields

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 etters 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.

References

External links

Prime Curios! 28
from the Prime Pages

{{Integers, zero

Integers