239 (number)
Encyclopedia
239 is the natural number
following 238 and preceding 240
.
. The next is 241, with which it forms a pair of twin prime
s. 239 is a Sophie Germain prime
and a Newman–Shanks–Williams prime. It is an Eisenstein prime
with no imaginary part and real part of the form 3n − 1 (with no exponentiation implied). Because the next odd number, 241 is prime, 239 is a Chen prime
.
HAKMEM
(incidentally AI memo 239 of the MIT AI Lab) included an item on the properties of 239, including these:
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 238 and preceding 240
240 (number)
240 is the natural number following 239 and preceding 241.-In mathematics:With 20 divisors total , more than any previous number, 240 is a highly composite number, and it is also a refactorable number or tau number, since it has 20 divisors and 20 divides 240...
.
| Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite... |
Two hundred [and] thirty-nine |
| Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals... |
Two hundred [and] thirty-ninth |
| Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original... |
(prime number 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... ) |
| Roman numeral | CCXXXIX |
| Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2... |
11101111 |
| Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen... |
EF |
In mathematics
It is a prime numberPrime 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...
. The next is 241, with which it forms a pair of twin prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
s. 239 is a Sophie Germain prime
Sophie Germain prime
In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number...
and a Newman–Shanks–Williams prime. It is an Eisenstein prime
Eisenstein prime
In mathematics, an Eisenstein prime is an Eisenstein integerz = a + b\,\omega\qquadthat is irreducible in the ring-theoretic sense: its only Eisenstein divisors are the units , a + bω itself and its associates.The associates and the complex conjugate...
with no imaginary part and real part of the form 3n − 1 (with no exponentiation implied). Because the next odd number, 241 is prime, 239 is a Chen prime
Chen prime
A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....
.
HAKMEM
HAKMEM
HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" of the MIT AI Lab that describes a wide variety of hacks, primarily useful and clever algorithms for mathematical computation. There are also some schematic diagrams for hardware...
(incidentally AI memo 239 of the MIT AI Lab) included an item on the properties of 239, including these:
- When expressing 239 as a sum of square numberSquare numberIn 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...
s, 4 squares are required, which is the maximum that any integer can require; it also needs the maximum number (9) of positive cubeCube (arithmetic)In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplying by itself three times:...
s (23 is the only other such integer), and the maximum number (19) of fourth powers. - 239/(13)2 is a convergentConvergent (continued fraction)A convergent is one of a sequence of values obtained by evaluating successive truncations of a continued fraction The nth convergent is also known as the nth approximant of a continued fraction.-Representation of real numbers:...
of the continued fractionContinued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
of the square root of 2Square root of 2The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.Geometrically the square root of 2 is the...
, so that 2392 = 2 · 134 − 1. - Related to the above, πPi' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
/4 = 4 arctan(1/5) − arctan(1/239). - 239 · 4649 = 1111111, so 1/239 = 0.0041841 repeating, with period 7.
- 239 can be written as bn − bm − 1 for b = 2, 3, and 4, a fact evidenced by its binaryBinary numeral systemThe binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
representation 11101111, ternaryTernary numeral systemTernary is the base- numeral system. Analogous to a bit, a ternary digit is a trit . One trit contains \log_2 3 bits of information...
representation 22212, and quaternaryQuaternary numeral systemQuaternary is the base- numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation and the characteristics of the representations of...
representation 3233. - There are 239 primes < 1500.
- 239 is the largest integer n whose factorialFactorialIn mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
can be written as the product of distinct factors between n + 1 and 2n, both included.
In other fields
239 is also:- K239 is MozartWolfgang Amadeus MozartWolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...
's only work for two orchestraOrchestraAn orchestra is a sizable instrumental ensemble that contains sections of string, brass, woodwind, and percussion instruments. The term orchestra derives from the Greek ορχήστρα, the name for the area in front of an ancient Greek stage reserved for the Greek chorus...
s. - 239 is the atomic mass number of the most common isotope of plutoniumPlutoniumPlutonium is a transuranic radioactive chemical element with the chemical symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, forming a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation...
, Pu-239 - The years A.D. 239239Year 239 was a common year starting on Tuesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Gordianus and Aviola...
and 239 BC239 BCYear 239 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Turrinus and Falto...
. - 239Area code 239239 is the North American telephone area code for a large area of Southwest Florida. It includes Lee and Collier counties, small parts of Hendry and Charlotte counties and the Everglades National park in Mainland Monroe County. It was created as an area code split from area code 941...
is an area code representing part of FloridaFloridaFlorida is a state in the southeastern United States, located on the nation's Atlantic and Gulf coasts. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia and to the east by the Atlantic Ocean. With a population of 18,801,310 as measured by the 2010 census, it...
in the United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district... - 239 is a world famous lyceum of physics in mathematics in Saint-Petersburg, RussiaRussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
. - In The SimpsonsThe SimpsonsThe Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical parody of a middle class American lifestyle epitomized by its family of the same name, which consists of Homer, Marge, Bart, Lisa and Maggie...
episode "Homer's Night Out", HomerHomer SimpsonHomer Jay Simpson is a fictional character in the animated television series The Simpsons and the patriarch of the eponymous family. He is voiced by Dan Castellaneta and first appeared on television, along with the rest of his family, in The Tracey Ullman Show short "Good Night" on April 19, 1987...
weighs himself and resolves to exercise. Six months later he weighs himself again and again resolves to exercise. Both times he weighed exactly 239 pounds. His weight was also seen in a daydream in the episode King-Size HomerKing-Size Homer"King-Size Homer" is the seventh episode of The Simpsons seventh season. It originally aired on the Fox network in the United States on November 5, 1995. In the episode, Homer despises the nuclear plant's new exercise program, and decides to gain in order to claim a disability and work at home...