natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
, an
abundant number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...
, a
pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...
* In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate.
*
NASCAR
The National Association for Stock Car Auto Racing, LLC (NASCAR) is an American auto racing sanctioning and operating company that is best known for stock car racing. The privately owned company was founded by Bill France Sr. in 1948, and ...
runs 600 advertised miles in the
Coca-Cola 600
The Coca-Cola 600, originally the World 600, is an annual NASCAR Cup Series points race held at the Charlotte Motor Speedway in Concord, North Carolina, on a Sunday during Memorial Day weekend. The first race, held in 1960, was also the first on ...
, its longest race.
* The
Fiat 600
The Fiat 600 ( it, Seicento, ) is a rear-engine, water-cooled city car, manufactured and marketed by Fiat from 1955 to 1969 — offered in two-door fastback sedan and four-door Multipla mini MPV body styles.
Measuring only long, its all-n ...
is a car, the
SEAT 600
The SEAT 600 is a city car made in Spain by SEAT from May 1957 until August 1973 under licence from Fiat. It helped to start the Spanish miracle (economic boom of 1959–1973) that came at the end of the slow recovery from the Spanish Civil War. ...
its Spanish version.
Integers from 601 to 699
600s
* 601 = prime number,
centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by th ...
* 602 = 2 × 7 × 43,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
Phoenix, AZ
Phoenix ( ; nv, Hoozdo; es, Fénix or , yuf-x-wal, Banyà:nyuwá) is the capital and most populous city of the U.S. state of Arizona
Arizona ( ; nv, Hoozdo Hahoodzo ; ood, Alĭ ṣonak ) is a state in the Southwestern United Stat ...
along with
480
__NOTOC__
Year 480 (Roman numerals, CDLXXX) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Basilius without colleague (or, less frequ ...
New Hampshire
New Hampshire is a state in the New England region of the northeastern United States. It is bordered by Massachusetts to the south, Vermont to the west, Maine and the Gulf of Maine to the east, and the Canadian province of Quebec to the nor ...
* 604 = 22 × 151,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky)
* 605 = 5 × 112, Harshad number, sum of the nontriangular numbers between the two successive
triangular numbers
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), admirable number
* 607 – prime number, sum of three consecutive primes (197 + 199 + 211),
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...
Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...
exponent
* 608 = 25 × 19,
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...
(608) = 0,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
,
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
,
Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
. Also a kind of telephone wall socket used in Australia.
* 611 = 13 × 47, sum of the three standard board sizes in Go (92 + 132 + 192), the 611th
tribonacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by:
:F_n =
\begin
0 & n = 0 \\
1 & n = 1 \\
F_ + F_ & n > 1
\end
That is, after two starting values, each number is the sum of the two preceding numbers.
The Fibonacci seque ...
is prime
* 612 = 22 × 32 × 17, Harshad number, Zuckerman number , area code for
Minneapolis, MN
Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with list of lakes in Minneapolis, thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. ...
* 613 = prime number, first number of
prime triple
In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form or . With the exceptions of and , this is the closest possible grouping of ...
(''p'', ''p'' + 4, ''p'' + 6), middle number of
sexy prime
In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and .
The term "sexy prime" is a pun stemming from the Latin word for six: .
If o ...
Centered square number
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...
with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a
lucky number
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...
, index of prime Lucas number.
** In
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...
the number 613 is very significant, as its metaphysics, the
Kabbalah
Kabbalah ( he, קַבָּלָה ''Qabbālā'', literally "reception, tradition") is an esoteric method, discipline and school of thought in Jewish mysticism. A traditional Kabbalist is called a Mekubbal ( ''Məqūbbāl'' "receiver"). The defin ...
, views every complete entity as divisible into 613 parts: 613 parts of every
Sefirah
Sefirot (; he, סְפִירוֹת, translit=Səfīrōt, Tiberian: '), meaning '' emanations'', are the 10 attributes/emanations in Kabbalah, through which Ein Sof (The Infinite) reveals itself and continuously creates both the physical realm an ...
Torah
The Torah (; hbo, ''Tōrā'', "Instruction", "Teaching" or "Law") is the compilation of the first five books of the Hebrew Bible, namely the books of Genesis, Exodus, Leviticus, Numbers and Deuteronomy. In that sense, Torah means the ...
Red Holzman
William "Red" Holzman (August 10, 1920 – November 13, 1998) was an American professional basketball player and coach. He is best known as the head coach of the New York Knicks of the National Basketball Association (NBA) from 1967 to ...
's 613 victories.
* 614 = 2 × 307,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
Emil Fackenheim
Emil Ludwig Fackenheim (22 June 1916 – 18 September 2003) was a Jewish philosopher and Reform rabbi.
Born in Halle, Germany, he was arrested by Nazis on the night of 9 November 1938, known as Kristallnacht. Briefly interned at the Sachsenhause ...
, the number of Commandments in Judaism should be 614 rather than the traditional 613.
* 615 = 3 × 5 × 41,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
* 616 = 23 × 7 × 11,
Padovan number
In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values
:P(0)=P(1)=P(2)=1,
and the recurrence relation
:P(n)=P(n-2)+P(n-3).
The first few values of ''P''(''n'') are
:1, 1, 1, 2, 2, 3, 4, 5 ...
, balanced number, an alternative value for the Number of the Beast (more commonly accepted to be
666
666 may refer to:
* 666 (number)
* 666 BC, a year
* AD 666, a year
* The number of the beast, a reference in the Book of Revelation in the New Testament
Places
* 666 Desdemona, a minor planet in the asteroid belt
* U.S. Route 666, an America ...
).
* 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137),
Chen prime
A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem.
The Chen primes are named after Chen Jingru ...
,
Eisenstein prime
In mathematics, an Eisenstein prime is an Eisenstein integer
: z = a + b\,\omega, \quad \text \quad \omega = e^,
that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...
with no imaginary part, number of compositions of 17 into distinct parts, prime index prime, index of prime Lucas number
**
Area code 617
Area codes 617 and 857 are the North American area codes serving Boston and several surrounding communities in Massachusetts—such as Brookline, Cambridge, Newton and Quincy ( LATA code 128).
The main area code, 617, was one of the orig ...
, a telephone area code covering the metropolitan Boston area.
* 618 = 2 × 3 × 103,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
* 620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97). The sum of the first 620 primes is itself prime.
* 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field
* 622 = 2 × 311,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the od ...
, 1-
automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base b, a natura ...
,
Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, pa ...
since 625 = 56−2
* 626 = 2 × 313,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, 2-Knödel number. Stitch's experiment number.
* 627 = 3 × 11 × 19, sphenic number, number of integer
partitions
Partition may refer to:
Computing Hardware
* Disk partitioning, the division of a hard disk drive
* Memory partition, a subdivision of a computer's memory, usually for use by a single job
Software
* Partition (database), the division of a ...
of 20,
Smith number
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-f ...
* 628 = 22 × 157,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
* 630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113),
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
,
hexagonal number
A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...
,
sparsely totient number In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, ''n'', is sparsely totient if for all ''m'' > ''n'',
:\varphi(m)>\varphi(n)
where \varphi is Euler's totient function. The first few sparsely toti ...
, Harshad number, balanced number
* 631 =
Cuban prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''.
First series
This is the first of these equations:
:p = \frac,\ x = ...
number,
centered triangular number
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.
The followin ...
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as
: 1, 2, 8, 9, 12, 18, ...
, number of 13-bead necklaces with 2 colors
* 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223),
Blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...
; also, in the title of the movie ''
633 Squadron
''633 Squadron'' is a 1964 British / American war film directed by Walter Grauman and starring Cliff Robertson, George Chakiris, and Maria Perschy. The plot, which involves the exploits of a fictional World War II British bomber squadron, wa ...
''
* 634 = 2 × 317,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, Smith number
* 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts
** "Project 635", the Irtysh River diversion project in China involving a
dam
A dam is a barrier that stops or restricts the flow of surface water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for activities such as irrigation, human consumption, industrial use ...
and a
canal
Canals or artificial waterways are waterways or engineered channels built for drainage management (e.g. flood control and irrigation) or for conveyancing water transport vehicles (e.g. water taxi). They carry free, calm surface flo ...
decagonal number
A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...
* 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167),
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
,
centered heptagonal number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...
* 639 = 32 × 71, sum of the first twenty primes, also
ISO 639
ISO 639 is a set of standards by the International Organization for Standardization that is concerned with representation of names for languages and language groups.
It was also the name of the original standard, approved in 1967 (as ''ISO 639/R ...
is the
ISO
ISO is the most common abbreviation for the International Organization for Standardization.
ISO or Iso may also refer to: Business and finance
* Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007
* Iso ...
's standard for codes for the representation of
language
Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as
: 1, 2, 8, 9, 12, 18, ...
, hexadecagonal number, number of 1's in all partitions of 24 into odd parts, number of acres in a square mile
* 641 = prime number,
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...
Fermat number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
:F_ = 2^ + 1,
where ''n'' is a non-negative integer. The first few Fermat numbers are:
: 3, 5, 17, 257, 65537, 42949672 ...
), Chen prime, Eisenstein prime with no imaginary part,
Proth prime
A Proth number is a natural number ''N'' of the form N = k \times 2^n +1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician François ...
* 642 = 2 × 3 × 107 = 14 + 24 + 54,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
, admirable number
* 643 = prime number, largest prime factor of 123456
* 644 = 22 × 7 × 23,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
umask
In computing, umask is a command that determines the settings of a mask that controls how file permissions are set for newly created files. It may also affect how the file permissions are changed explicitly. is also a function that sets the ma ...
octagonal number
An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are
: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 34 ...
, Smith number,
Fermat pseudoprime
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.
Definition
Fermat's little theorem states that if ''p'' is prime and ''a'' is coprime to ''p'', then ''a'p''− ...
to base 2, Harshad number
* 646 = 2 × 17 × 19, sphenic number, also
ISO 646
ISO/IEC 646 is a set of ISO/IEC standards, described as ''Information technology — ISO 7-bit coded character set for information interchange'' and developed in cooperation with ASCII at least since 1964. Since its first edition in ...
is the ISO's standard for international 7-bit variants of
ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
, number of permutations of length 7 without rising or falling successions
* 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3647 - 2647 is prime
* 648 = 23 × 34 A331452(7, 1) Harshad number,
Achilles number
An Achilles number is a number that is powerful but not a perfect power.
A positive integer is a powerful number if, for every prime factor of , is also a divisor. In other words, every prime factor appears at least squared in the factoriza ...
, area of a square with diagonal 36
* 649 = 11 × 59,
Blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...
,
nonagonal number A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the constr ...
* 652 = 22 × 163, maximal number of regions by drawing 26 circles
* 653 = prime number, Sophie Germain prime, balanced prime, Chen prime, Eisenstein prime with no imaginary part
* 654 = 2 × 3 × 109, sphenic number,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, Smith number,admirable number
* 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid
* 656 = 24 × 41 = . In
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...
, 656 is the number of times that
Jerusalem
Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...
is mentioned in the
Hebrew Bible
The Hebrew Bible or Tanakh (;"Tanach" '' Old Testament.
* 657 = 32 × 73, the largest known number not of the form ''a''2+''s'' with ''s'' a
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime ...
* 658 = 2 × 7 × 47,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
,
untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...
* 659 = prime number, Sophie Germain prime, sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number, Eisenstein prime with no imaginary part, strictly non-palindromic number
660s
* 660 = 22 × 3 × 5 × 11
**Sum of four consecutive primes (157 + 163 + 167 + 173).
**Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127).
**Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101).
**Sparsely totient number.
**Sum of 11th row when writing the natural numbers as a triangle.
** Harshad number.
* 661 = prime number
**Sum of three consecutive primes (211 + 223 + 227).
**Mertens function sets new low of −11 which stands until 665.
**
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle arou ...
number of the form .
** Hexagram number of the form i.e. a
star number
A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on.
The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n'' − 1) + 1. The ...
.
* 662 = 2 × 331,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, member of
Mian–Chowla sequence
In mathematics, the Mian–Chowla sequence is an integer sequence defined
recursively in the following way. The sequence starts with
:a_1 = 1.
Then for n>1, a_n is the smallest integer such that every pairwise sum
:a_i + a_j
is distinct, for ...
* 663 = 3 × 13 × 17,
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
, Smith number
* 664 = 23 × 83,
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as
: 1, 2, 8, 9, 12, 18, ...
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon
*
666
666 may refer to:
* 666 (number)
* 666 BC, a year
* AD 666, a year
* The number of the beast, a reference in the Book of Revelation in the New Testament
Places
* 666 Desdemona, a minor planet in the asteroid belt
* U.S. Route 666, an America ...
= 2 × 32 × 37,
repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.
Example ...
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
* 669 = 3 × 223,
blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/tal ...
670s
* 670 = 2 × 5 × 67, sphenic number,
octahedral number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ''n''th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahed ...
,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
harmonic divisor number
In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are:
: 1, 6, 2 ...
, Zuckerman number, admirable number
* 673 = prime number, Proth prime
* 674 = 2 × 337,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
Achilles number
An Achilles number is a number that is powerful but not a perfect power.
A positive integer is a powerful number if, for every prime factor of , is also a divisor. In other words, every prime factor appears at least squared in the factoriza ...
* 676 = 22 × 132 = 262, palindromic square
* 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10
* 678 = 2 × 3 × 113, sphenic number,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, number of surface points of an octahedron with side length 13, admirable number
* 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5
680s
* 680 = 23 × 5 × 17,
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
* 681 = 3 × 227, centered pentagonal number
* 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzl strikketoy
* 683 = prime number, Sophie Germain prime, sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part,
Wagstaff prime
In number theory, a Wagstaff prime is a prime number of the form
:
where ''p'' is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the ...
* 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32
* 685 = 5 × 137, centered square number
* 686 = 2 × 73,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, number of multigraphs on infinite set of nodes with 7 edges
* 687 = 3 × 229, 687 days to orbit the sun (
Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
) D-number
* 688 = 24 × 43, Friedman number since 688 = 8 × 86, 2-
automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base b, a natura ...
* 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number
690s
* 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, Smith number, Harshad number
**
ISO 690
ISO 690 is an ISO standard governing bibliographic references in different kinds of documents, including electronic documents. This international standard specifies the bibliographic elements that need to be included in references to published ...
is the ISO's standard for bibliographic references
* 691 = prime number, (negative) numerator of the
Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...
divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (includin ...
σ11 are related by the remarkable congruence τ(''n'') ≡ σ11(''n'') (mod 691).
** In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.
* 692 = 22 × 173, number of partitions of 48 into powers of 2
* 693 = 32 × 7 × 11, triangular matchstick number, the number of sections in
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is con ...
's ''
Philosophical Investigations
''Philosophical Investigations'' (german: Philosophische Untersuchungen) is a work by the philosopher Ludwig Wittgenstein, published posthumously in 1953.
''Philosophical Investigations'' is divided into two parts, consisting of what Wittgens ...
''.
* 694 = 2 × 347, centered triangular number,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
* 695 = 5 × 139, 695!! + 2 is prime.
* 696 = 23 × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice
* 697 = 17 × 41,
cake number
In mathematics, the cake number, denoted by ''Cn'', is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly ''n'' planes. The cake number is so-called because one may imagine each partition of the cu ...
; the number of sides of Colorado
* 698 = 2 × 349,
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
, sum of squares of two primes
* 699 = 3 × 233, D-number