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38 (number)
Encyclopedia
This article discusses the number thirty-eight. For the year 38 CE, see 38
. For other uses of 38, see 38 (disambiguation)
38 (thirty-eight) is the natural number
following 37
and preceding 39
.
and the 7th in the {2.q} family. It is the initial member of the third distinct semiprime
pair (38, 39
).
38 has an aliquot sum of 22
which is itself a distinct semiprime
In fact 38 is the first number to be at the head of a chain of four distinct semiprime
s in its 8 member aliquot sequence (38, 22
, 14
, 10
, 8, 7, 1, 0
). 38 is the 8th member of the 7-aliquot tree.
38! - 1 yields 523022617466601111760007224100074291199999999, which is the 16th factorial prime
.
There is no answer to the equation φ
(x) = 38, making 38 a nontotient
.
38 is the sum of the squares
of the first three prime
s.
37
and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
38 is the largest even number which cannot be written as the sum of two odd composite numbers.
There are only two normal magic hexagon
s, order 1 (which is trivial) and order 3. The sum of each row of an order 3 magic hexagon is 38.
Thirty-eight is also:
38
Year 38 was a common year starting on Wednesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Iulianus and Asprenas...
. For other uses of 38, see 38 (disambiguation)
38 (disambiguation)
38 is the year 38 CE.38 or thirty-eight may also refer to:*38 *38 BCE, the year 38 BCE*.38 caliber firearms and cartridges**The .38 Special revolver cartridge...
38 (thirty-eight) is the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 37
37 (number)
37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
and preceding 39
39 (number)
39 is the natural number following 38 and preceding 40.- In mathematics :Thirty-nine is the sum of five consecutive primes and the sum of the first three powers of 3...
.
In mathematics
38 is the 11th distinct semiprimeSemiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
and the 7th in the {2.q} family. It is the initial member of the third distinct semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
pair (38, 39
39 (number)
39 is the natural number following 38 and preceding 40.- In mathematics :Thirty-nine is the sum of five consecutive primes and the sum of the first three powers of 3...
).
38 has an aliquot sum of 22
22 (number)
22 is the natural number following 21 and preceding 23.- In mathematics :Twenty-two is an even composite number, its proper divisors being 1, 2 and 11....
which is itself a distinct semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
In fact 38 is the first number to be at the head of a chain of four distinct semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
s in its 8 member aliquot sequence (38, 22
22 (number)
22 is the natural number following 21 and preceding 23.- In mathematics :Twenty-two is an even composite number, its proper divisors being 1, 2 and 11....
, 14
14 (number)
14 is the natural number following 13 and preceding 15.In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 vs 40...
, 10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, 8, 7, 1, 0
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
). 38 is the 8th member of the 7-aliquot tree.
38! - 1 yields 523022617466601111760007224100074291199999999, which is the 16th factorial prime
Factorial prime
A factorial prime is a prime number that is one less or one more than a factorial . The first few factorial primes are:n! − 1 is prime for :n! + 1 is prime for :...
.
There is no answer to the equation φ
Euler's totient function
In number theory, the totient \varphi of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n In number theory, the totient \varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that...
(x) = 38, making 38 a nontotient
Nontotient
In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...
.
38 is the sum of the squares
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
of the first three prime
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s.
37
37 (number)
37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
38 is the largest even number which cannot be written as the sum of two odd composite numbers.
There are only two normal magic hexagon
Magic hexagon
A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant. A normal magic hexagon contains the consecutive integers from 1 to...
s, order 1 (which is trivial) and order 3. The sum of each row of an order 3 magic hexagon is 38.
Astronomy
- The Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M38Messier 38Messier 38 is an open cluster in the Auriga constellation.It was discovered by Giovanni Batista Hodierna before 1654 and independently found by Le Gentil in 1749...
, a magnitude 7.0 open clusterOpen clusterAn open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, and many more are thought to exist...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
AurigaAuriga (constellation)Auriga is a constellation in the northern sky. Its name is Latin for 'charioteer' and its stars form a shape that has been associated with the pointed helmet of a charioteer. It was one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and remains among the 88 modern... - The Saros number of
- the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on -1729 June 26 and ended on -431 August 14. The duration of Saros series 38 was 1298.1 years, and it contained 73 solar eclipses. - the lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on -1408 April 16 and ended on -111 June 3. The duration of Saros series 38 was 1298.1 years, and it contained 73 lunar eclipses.
- the solar eclipse
- The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 38NGC 38NGC 38 is a spiral galaxy in the constellation Pisces.-External links:*...
, a spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation PiscesPisces (constellation)Pisces is a constellation of the zodiac. Its name is the Latin plural for fish, and its symbol is . It lies between Aquarius to the west and Aries to the east... - The 38th parallel north38th parallel northThe 38th parallel north is a circle of latitude that is 38 degrees north of the Earth's equatorial plane. It crosses Europe, the Mediterranean Sea, Asia, the Pacific Ocean, North America, and the Atlantic Ocean...
is pre-Korean WarKorean WarThe Korean War was a conventional war between South Korea, supported by the United Nations, and North Korea, supported by the People's Republic of China , with military material aid from the Soviet Union...
boundary between North KoreaNorth KoreaThe Democratic People’s Republic of Korea , , is a country in East Asia, occupying the northern half of the Korean Peninsula. Its capital and largest city is Pyongyang. The Korean Demilitarized Zone serves as the buffer zone between North Korea and South Korea...
and South KoreaSouth KoreaThe Republic of Korea , , is a sovereign state in East Asia, located on the southern portion of the Korean Peninsula. It is neighbored by the People's Republic of China to the west, Japan to the east, North Korea to the north, and the East China Sea and Republic of China to the south...
.
In mythology
- The number 38 was especially prominent in Norse mythologyNorse mythologyNorse mythology, a subset of Germanic mythology, is the overall term for the myths, legends and beliefs about supernatural beings of Norse pagans. It flourished prior to the Christianization of Scandinavia, during the Early Middle Ages, and passed into Nordic folklore, with some aspects surviving...
. The number was said to represent unnatural bravery, characteristic of the legendary heroes of Norse sagasSagàsSagàs is a small town and municipality located in Catalonia, in the comarca of Berguedà. It is located in the geographical area of the pre-Pyrenees.-Population:...
. Most legendary sagas were divided into 38 chapters, and the number often recurred throughout stories, with the heroes combating giants or other beasts in groups of 38. The number came to be adopted by the Hardrada clan, and was displayed on their crest in the form of 38 ravens set around 38 outward-facing arrows. - The number was also significant in Egyptian mythologyEgyptian mythologyAncient Egyptian religion was a complex system of polytheistic beliefs and rituals which were an integral part of ancient Egyptian society. It centered on the Egyptians' interaction with a multitude of deities who were believed to be present in, and in control of, the forces and elements of nature...
, as it was the characteristic number of AnubisAnubisAnubis is the Greek name for a jackal-headed god associated with mummification and the afterlife in ancient Egyptian religion. In the ancient Egyptian language, Anubis is known as Inpu . According to the Akkadian transcription in the Amarna letters, Anubis' name was vocalized as Anapa...
, the jackal-headed god of death and mummificationMummyA mummy is a body, human or animal, whose skin and organs have been preserved by either intentional or incidental exposure to chemicals, extreme coldness , very low humidity, or lack of air when bodies are submerged in bogs, so that the recovered body will not decay further if kept in cool and dry...
. Egyptian pharaohs were often buried with 38 statues of cat guardians, and their sarcophagi were adorned with 38 ankhAnkhThe ankh , also known as key of life, the key of the Nile or crux ansata, was the ancient Egyptian hieroglyphic character that read "eternal life", a triliteral sign for the consonants ʻ-n-ḫ...
s.
In other fields
- The number of slots on an American RouletteRouletteRoulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
wheel (0, 00, and 1 through 36; European roulette does not use the 00 slot and has only 37 slots) - The number of games that each team in the current English PremiershipFA Premier LeagueThe Premier League is an English professional league for association football clubs. At the top of the English football league system, it is the country's primary football competition. Contested by 20 clubs, it operates on a system of promotion and relegation with The Football League. The Premier...
, the top division in English Association Football, plays in a season - Bill C-38 legalized same-sex marriage in CanadaCanadaCanada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
- The number of years it took the Israelites to travel from Kadesh Barnea to the ZeredWadi ZeredThe Wadi Zered is a wadi in western Jordan. Also known in Jordan as Wadi-Hasa. In ancient times it was the boundary between Moab and Edom. Mentioned in the Torah ....
valley in DeuteronomyDeuteronomyThe Book of Deuteronomy is the fifth book of the Hebrew Bible, and of the Jewish Torah/Pentateuch...
. - A "38" is often the name for a snub nose .38 caliber revolver
- Name of the southern rockSouthern rockSouthern rock is a subgenre of rock music, and genre of Americana. It developed in the Southern United States from rock and roll, country music, and blues, and is focused generally on electric guitar and vocals...
band 38 Special - The 38 class is the most famous class of steam locomotiveSteam locomotiveA steam locomotive is a railway locomotive that produces its power through a steam engine. These locomotives are fueled by burning some combustible material, usually coal, wood or oil, to produce steam in a boiler, which drives the steam engine...
used in New South WalesNew South WalesNew South Wales is a state of :Australia, located in the east of the country. It is bordered by Queensland, Victoria and South Australia to the north, south and west respectively. To the east, the state is bordered by the Tasman Sea, which forms part of the Pacific Ocean. New South Wales... - The number of the French department IsèreIsèreIsère is a department in the Rhône-Alpes region in the east of France named after the river Isère.- History :Isère is one of the original 83 departments created during the French Revolution on March 4, 1790. It was created from part of the former province of Dauphiné...
- There are 38 surviving plays written by William ShakespeareWilliam ShakespeareWilliam Shakespeare was an English poet and playwright, widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's national poet and the "Bard of Avon"...
. - The gate of the sci-fi TV series Stargate SG-1Stargate SG-1Stargate SG-1 is a Canadian-American adventure and military science fiction television series and part of Metro-Goldwyn-Mayer's Stargate franchise. The show, created by Brad Wright and Jonathan Glassner, is based on the 1994 feature film Stargate by Dean Devlin and Roland Emmerich...
can stay open a maximum of 38 minutes. - In Taiwan, "3, 8", but not "38", is slang for stupid/idiot.