500 (number)
Encyclopedia
500 is the natural number
following 499 and preceding 501.
has its own article.
----
502 = 2 × 251
, also a proposed HTTP status code for indicating server is temporarily overloaded, SMTP status code meaning command not implemented
----
503 prime number
, safe prime
, sum of three consecutive primes (163 + 167 + 173), sum of the cubes of the first four primes, Chen prime
, Eisenstein prime
with no imaginary part, also a proposed HTTP status code indicating a gateway time-out, SMTP status code meaning bad sequence of commands
----
504 = 23 × 32 × 7, tribonacci number, semi-meandric number, refactorable number, Harshad number, also SMTP status code meaning command parameter not implemented
----
505 = 5 × 101, also model number of Levi's jeans
, model number of
This number is the magic constant
of n×n normal magic square
and n-queens problem
for n = 10.
New Mexico – Before October 7, 2007, The United States state of New Mexico had a single area code of 505. The state was, and still is, referred to as 'the 505' in slang.
----
506 = 2 × 11 × 23, sphenic number
, square pyramidal number
, pronic number
, Harshad number
----
507 = 3 × 132
----
508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137)
----
509 prime number, Sophie Germain prime
, smallest Sophie Germain prime to start a 4-term Cunningham chain
of the first kind {509, 1019, 2039, 4079}, Chen prime, Eisenstein prime with no imaginary part, highly cototient number
----
510 = 2 × 3 × 5 × 17, sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), sum of ten consecutive primes (31 + 37 + 43 + 47 + 53 + 59 + 61 + 67 + 71), sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 43 + 47 + 53 + 59 + 61 + 67), nontotient
, sparsely totient number, Harshad number.
----
511 = 7 × 73, Harshad number
511 is:
----
512 = 29, power of two
, cube of 8, Leyland number
, Dudeney number
, Harshad number
----
513 = 33 × 19, Harshad number
----
514 = 2 × 257, centered triangular number
, nontotient
----
515 = 5 × 103, sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)
----
516 = 22 × 3 × 43, nontotient, untouchable number
, refactorable number, Harshad number
----
517 = 11 × 47, sum of five consecutive primes (97 + 101 + 103 + 107 + 109), Smith number
----
518 = 2 × 7 × 37 = 51 + 12 + 83 (a property shared with 175
and 598), sphenic number, nontotient, untouchable number, Harshad number
----
519 = 3 × 173, sum of three consecutive primes (167 + 173 + 179)
----
520 = 23 × 5 × 13, untouchable number
----
521 Lucas prime, Chen prime, Eisenstein prime with no imaginary part
----
522 = 2 × 32 × 29, sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101), Harshad number
----
523 prime number, sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89)
----
524 = 22 × 131
----
525 = 3 × 52 × 7, also the number of scan lines in the NTSC
television standard.
----
526 = 2 × 263, centered pentagonal number
, nontotient, Smith number
----
527 = 17 × 31, also the section of the US Tax Code regulating soft money political campaigning (see 527 group
s)
----
528 = 24 × 3 × 11, triangular number
----
529 = 232, centered octagonal number
, also Section 529 of the IRS tax code organizes 529 plan
s to encourage saving for higher education.
----
530 = 2 × 5 × 53, sphenic number
, nontotient, sum of totient function for first 41 integers, untouchable number
, sum of the first three perfect numbers.
----
531 = 32 × 59, Harshad number
----
532 = 22 × 7 × 19, nontotient
----
533 = 13 × 41, sum of three consecutive primes (173 + 179 + 181), sum of five consecutive primes (101 + 103 + 107 + 109 + 113)
----
534 = 2 × 3 × 89, sphenic number, sum of four consecutive primes (127 + 131 + 137 + 139), nontotient
----
535 = 5 × 107, Smith number,
for 
; this polynomial plays an essential role in Apéry's proof
that
is irrational.
535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the June Fourth Incident.
----
536 = 23 × 67, the number of ways to arrange the pieces of the stomachion puzzle into a square, not counting rotation or reflection, refactorable number; lowest happy number
beginning with the digit 5.
----
537 = 3 × 179, Mertens function(537) = 0
----
538 = 2 × 269, open meandric number, nontotient; also, the total number of votes in the Electoral College of the United States
----
539 = 72 × 11
----
540 = 22 × 33 × 5, untouchable number, decagonal number
, Harshad number
----
541 is the 100th prime, a lucky prime, a Chen prime and a star number
. Mertens function(541) = 0.
----
542 = 2 × 271, nontotient, sum of totient function for first 42 integers
----
543 = 3 × 181
----
544 = 25 × 17
----
545 = 5 × 109, centered square number
----
546 = 2 × 3 × 7 × 13, sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)
----
547 prime number, cuban prime, centered hexagonal number
, centered heptagonal number
----
548 = 22 × 137, nontotient
, every positive integer is the sum of at most 548 ninth powers; also the default port for the Apple Filing Protocol
----
549 = 32 × 61
----
550 = 2 × 52 × 11, pentagonal pyramidal number
, nontotient, Harshad number, also SMTP status code meaning the requested action was not taken because the mailbox is unavailable
----
551 = 19 × 29, sum of three consecutive primes (179 + 181 + 191), SMTP status code meaning user is not local
----
552 = 23 × 3 × 23, sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103), sum of ten consecutive primes (37 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), pronic number, untouchable number, Harshad number; model number of , SMTP status code meaning requested action aborted because the mailbox is full
----
553 = 7 × 79, sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79); model number of , SMTP status code meaning requested action aborted because of faulty mailbox name
----
554 = 2 × 277, Mertens function(554) = 6 a record high that stands until 586, nontotient, also SMTP status code meaning transaction failed
----
555
is a sphenic number
, a repdigit
and a Harshad number
----
556 = 22 × 139, sum of four consecutive primes (131 + 137 + 139 + 149). But it is never the sum of the proper divisors of any integer, making it an untouchable number
; happy number; model number of .
----
557 prime number, Chen prime, Eisenstein prime with no imaginary part
----
558 = 2 × 32 × 31, nontotient, Harshad number. The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993). Also, 558 is in the title of the Star Trek: Deep Space Nine
episode "The Siege of AR-558
"
----
559 = 13 × 43, sum of five consecutive primes (103 + 107 + 109 + 113 + 127), sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97), nonagonal number, centered cube number
, model number of
----
560 = 24 × 5 × 7, tetrahedral number
, refactorable number
----
561 = 3 × 11 × 17, triangular number, hexagonal number
, the first Carmichael number
----
562 = 2 × 281, Smith number, untouchable number, sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
----
563 103rd prime number, safe prime, Wilson prime
, Chen prime, Eisenstein prime with no imaginary part, balanced prime, strictly non-palindromic number, sexy prime
, happy number
----
564 = 22 × 3 × 47, sum of a twin prime (281 + 283), refactorable number
----
565 = 5 × 113, sum of three consecutive primes (181 + 191 + 193), member of the Mian–Chowla sequence, happy number
----
566 = 2 × 283, nontotient, happy number
----
567 = 34 × 7
----
568 = 23 × 71, sum of the first nineteen primes, refactorable number, smallest number whose seventh power is the sum of 7 seventh powers, the room number booked by Benjamin Braddock in the film 1967 film The Graduate
, the name of the Student Union bar at Imperial College London
----
569 prime number, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number
----
570 = 2 × 3 × 5 × 19
----
571 prime number, Chen prime, centered triangular number, model number of ]] which appeared in the 2000 movie U-571
----
572 = 22 × 11 × 13, nontotient
----
573 = 3 × 191, model number of , known as the Konami number
because Konami can be represented by 573's Goroawase form of "ko-na-mi".
----
574 = 2 × 7 × 41, sphenic number, nontotient
----
575 = 52 × 23
----
576 = 26 × 32 = 242, sum of four consecutive primes (137 + 139 + 149 + 151), highly totient number
, Smith number, untouchable number, Harshad number. 576 is also four-dozen sets of a dozen, which makes it 4 gross.
----
577 prime number, Proth prime
----
578 = 2 × 172, nontotient
----
579 = 3 × 193, a ménage number
----
580 = 22 × 5 × 29, sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107)
----
581 = 7 × 83, sum of three consecutive primes (191 + 193 + 197)
----
582 = 2 × 3 × 97, sphenic number, sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), nontotient
----
583 = 11 × 53
----
584 = 23 × 73, untouchable number, sum of totient function for first 43 integers, refactorable number
----
585 = 32 × 5 × 13
When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".
----
586
= 2 × 293, Mertens function(586) = 7 a record high that stands until 1357; also the number of several popular personal computer processors (such as the Intel)
----
587 prime number, safe prime, sum of five consecutive primes (107 + 109 + 113 + 127 + 131), Chen prime, Eisenstein prime with no imaginary part. Outgoing port for email
message submission
.
----
588 = 22 3 × 72, Smith number, Harshad number
----
589 = 19 × 31, sum of three consecutive primes (193 + 197 + 199)
----
590 = 2 × 5 × 59, sphenic number, nontotient
----
591 = 3 × 197
----
592 = 24 × 37, Harshad number
----
593
prime number, Sophie Germain prime
, sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101), sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Eisenstein prime
with no imaginary part, balanced prime, Leyland number, member of the Mian–Chowla sequence, strictly non-palindromic number
----
594 = 2 × 33 × 11, sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number
----
595 = 5 × 7 × 17, sphenic number, triangular number, centered nonagonal number
----
596 = 22 × 149, sum of four consecutive primes (139 + 149 + 151 + 157), nontotient
----
597 = 3 × 199
----
598 = 2 × 13 × 23 = 51 + 92 + 83, sphenic number
----
599 prime number, Chen prime, Eisenstein prime with no imaginary part.
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 499 and preceding 501.
Other fields
Five hundred is also- many NASCARNASCARThe National Association for Stock Car Auto Racing is a family-owned and -operated business venture that sanctions and governs multiple auto racing sports events. It was founded by Bill France Sr. in 1947–48. As of 2009, the CEO for the company is Brian France, grandson of the late Bill France Sr...
races often use the number 500 at the end of their race names (i.e. Daytona 500Daytona 500The Daytona 500 is a -long NASCAR Sprint Cup Series race held annually at the Daytona International Speedway in Daytona Beach, Florida. It is one of four restrictor plate races on the Cup schedule....
), to denote the length of the race (in mileMileA mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...
s, kilometers or laps). - the longest advertised distance of the IndyCar Series and its premier race, the Indianapolis 500Indianapolis 500The Indianapolis 500-Mile Race, also known as the Indianapolis 500, the 500 Miles at Indianapolis, the Indy 500 or The 500, is an American automobile race, held annually, typically on the last weekend in May at the Indianapolis Motor Speedway in Speedway, Indiana...
. - an Italian car, the Fiat 500Fiat 500The Fiat 500 is a car produced by the Fiat company of Italy between 1957 and 1975, with limited production of the Fiat 500 K estate continuing until 1977. The car was designed by Dante Giacosa....
, or a number of cars in the United States built by Ford: the Ford Five HundredFord Five HundredThe Ford Five Hundred is a full-size sedan that was produced by the Ford Motor Company during the 2005 to 2007 model years in North America. In North America, the name evoked the classic Fairlane 500 and Galaxie 500 models of the 1950s through 1970s.-Overview:The Five Hundred was introduced at the...
, Galaxie 500Ford GalaxieThe Ford Galaxie was a full-size car built in the United States by the Ford Motor Company for model years 1959 through 1974. The name was used for the top models in Ford’s full-size range from 1959 until 1961, in a marketing attempt to appeal to the excitement surrounding the Space Race...
and Custom 500. - a name of two different card games, see 500 (card game)500 (card game)500, Five Hundred, is a game devised in America shortly before 1900 and promoted by the United States Playing Card Company, who copyrighted and marketed the rules in 1904. The game can be played by two to six players but the most common form is for four players in partnerships although some sources...
for the trick taking game and 500 Rum500 Rum500 rum, also called pinochle rummy, Michigan rummy, rummy 500 or 500 rummy, is a popular variant of rummy. The game of canasta and several other games are believed to have developed from this popular form of rummy. The distinctive feature of 500 Rum is that each player scores the value of the...
for the rummy game. - (500) Days of Summer is a 20092009 in filmThe year 2009 saw the release of many films. Seven made the top 50 list of highest-grossing films, and the Academy of Motion Picture Arts and Sciences announced that as of this year, their Best Picture category would consist of ten nominees, rather than five .- Highest-grossing films :Please note...
film directed by Marc WebbMarc WebbMarc Preston Webb is an American music video, short film and major motion picture director. He directed the 2009 romantic comedy-drama Days of Summer and is currently directing the 2012 Spider-Man reboot The Amazing Spider-Man.-Life and career:Webb was born in Bloomington, Indiana, the son of... - an outdoor ball/disc game, see 500 (outdoor game)
- an HTTP status code for Internal Server Error
- an SMTPSimple Mail Transfer ProtocolSimple Mail Transfer Protocol is an Internet standard for electronic mail transmission across Internet Protocol networks. SMTP was first defined by RFC 821 , and last updated by RFC 5321 which includes the extended SMTP additions, and is the protocol in widespread use today...
status code meaning a syntax error has occurred due to unrecognized command - the years AD 500500Year 500 was a leap year starting on Saturday of the Julian calendar. At the time, it was known as the Year of the Consulship of Patricius and Hypatius...
, 500 BC. - the winning permillagePermilleA per mil or per mille is a tenth of a percent or one part per thousand. It is written with the sign ‰ , which looks like a percent sign with an extra zero at the end...
of a sports team with equal numbers of wins and losses. Such teams are often referred to as "500 teams".
Numbers from 501 to 599
501501 (number)
501 is the natural number following 500 and followed by 502.501 is the sum of the first eighteen primes....
has its own article.
----
502 = 2 × 251
251 (number)
251 is the natural number between 250 and 252. It is also a prime number.-In mathematics:251 is a regular prime, an Eisenstein prime, a Chen prime, a Gaussian prime, a Sophie Germain prime, and a sexy prime....
, also a proposed HTTP status code for indicating server is temporarily overloaded, SMTP status code meaning command not implemented
----
503 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...
, safe prime
Safe prime
A safe prime is a prime number of the form 2p + 1, where p is also a prime. The first few safe primes are...
, sum of three consecutive primes (163 + 167 + 173), sum of the cubes of the first four primes, 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....
, 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, also a proposed HTTP status code indicating a gateway time-out, SMTP status code meaning bad sequence of commands
----
504 = 23 × 32 × 7, tribonacci number, semi-meandric number, refactorable number, Harshad number, also SMTP status code meaning command parameter not implemented
----
505 = 5 × 101, also model number of Levi's jeans
Jeans
Jeans are trousers made from denim. Some of the earliest American blue jeans were made by Jacob Davis, Calvin Rogers, and Levi Strauss in 1873. Starting in the 1950s, jeans, originally designed for cowboys, became popular among teenagers. Historic brands include Levi's, Lee, and Wrangler...
, model number of
This number is the magic constant
Magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....
of n×n normal magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
and n-queens problem
Eight queens puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...
for n = 10.
New Mexico – Before October 7, 2007, The United States state of New Mexico had a single area code of 505. The state was, and still is, referred to as 'the 505' in slang.
----
506 = 2 × 11 × 23, sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...
, square pyramidal number
Square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...
, pronic number
Pronic number
A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...
, Harshad number
----
507 = 3 × 132
----
508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137)
----
509 prime number, 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...
, smallest Sophie Germain prime to start a 4-term Cunningham chain
Cunningham chain
In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes....
of the first kind {509, 1019, 2039, 4079}, Chen prime, Eisenstein prime with no imaginary part, highly cototient number
Highly cototient number
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...
----
510 = 2 × 3 × 5 × 17, sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), sum of ten consecutive primes (31 + 37 + 43 + 47 + 53 + 59 + 61 + 67 + 71), sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 43 + 47 + 53 + 59 + 61 + 67), 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,...
, sparsely totient number, Harshad number.
----
511 = 7 × 73, Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
511 is:
- 5-1-15-1-15-1-1, initially designated for road weather information, is a transportation and traffic information telephone hotline in some regions of the United States and Canada. Travelers can dial the three-digit telephone number 5-1-1 on traditional landline telephones and most mobile phones. It is an N11...
, a roadway status and transit information hotlineHotlineIn telecommunication, a hotline is a point-to-point communications link in which a call is automatically directed to the preselected destination without any additional action by the user when the end instrument goes off-hook...
in many metropolitan areas of the United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
. - Paul ErdősPaul ErdosPaul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
had 511 collaborators.
----
512 = 29, power of two
Power of two
In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....
, cube of 8, Leyland number
Leyland number
In number theory, a Leyland number is a number of the form xy + yx, where x and y are integers greater than 1. The first few Leyland numbers are...
, Dudeney number
Dudeney number
A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equal to the cube root of the number. There are exactly six such integers : 1 = 1 x 1 x 1 ; 1 = 1 512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2...
, Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
----
513 = 33 × 19, Harshad number
----
514 = 2 × 257, centered triangular number
Centered triangular number
A centered triangular number is a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers...
, nontotient
----
515 = 5 × 103, sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)
----
516 = 22 × 3 × 43, nontotient, untouchable number
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 ....
, refactorable number, Harshad number
----
517 = 11 × 47, sum of five consecutive primes (97 + 101 + 103 + 107 + 109), Smith number
Smith number
A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...
----
518 = 2 × 7 × 37 = 51 + 12 + 83 (a property shared with 175
175 (number)
175 is the natural number following 174 and preceding 176.-In mathematics:* 175 is an odd number* 175 is a composite number* 175 is a decagonal number, a figurate number that represents a decagon* 175 is a deficient number, as 73 is less than 175...
and 598), sphenic number, nontotient, untouchable number, Harshad number
----
519 = 3 × 173, sum of three consecutive primes (167 + 173 + 179)
----
520 = 23 × 5 × 13, untouchable number
----
521 Lucas prime, Chen prime, Eisenstein prime with no imaginary part
----
522 = 2 × 32 × 29, sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101), Harshad number
----
523 prime number, sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89)
----
524 = 22 × 131
----
525 = 3 × 52 × 7, also the number of scan lines in the NTSC
NTSC
NTSC, named for the National Television System Committee, is the analog television system that is used in most of North America, most of South America , Burma, South Korea, Taiwan, Japan, the Philippines, and some Pacific island nations and territories .Most countries using the NTSC standard, as...
television standard.
----
526 = 2 × 263, centered pentagonal 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...
, nontotient, Smith number
----
527 = 17 × 31, also the section of the US Tax Code regulating soft money political campaigning (see 527 group
527 group
A 527 organization or 527 group is a type of American tax-exempt organization named after "Section 527" of the U.S. Internal Revenue Code...
s)
----
528 = 24 × 3 × 11, triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
----
529 = 232, centered octagonal number
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...
, also Section 529 of the IRS tax code organizes 529 plan
529 plan
A 529 plan is a tax-advantaged investment vehicle in the United States designed to encourage saving for the future higher education expenses of a designated beneficiary.- Overview :529 plans are named after section 529 of the Internal Revenue Code...
s to encourage saving for higher education.
----
530 = 2 × 5 × 53, sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...
, nontotient, sum of totient function for first 41 integers, untouchable number
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 ....
, sum of the first three perfect numbers.
----
531 = 32 × 59, Harshad number
----
532 = 22 × 7 × 19, nontotient
----
533 = 13 × 41, sum of three consecutive primes (173 + 179 + 181), sum of five consecutive primes (101 + 103 + 107 + 109 + 113)
----
534 = 2 × 3 × 89, sphenic number, sum of four consecutive primes (127 + 131 + 137 + 139), nontotient
----
535 = 5 × 107, Smith number,
for ; this polynomial plays an essential role in Apéry's proofApéry's constant
In mathematics, Apéry's constant is a number that occurs in a variety of situations. It arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio using quantum electrodynamics...
that
is irrational.535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the June Fourth Incident.
----
536 = 23 × 67, the number of ways to arrange the pieces of the stomachion puzzle into a square, not counting rotation or reflection, refactorable number; lowest happy number
Happy number
A happy number is defined by the following process. Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 , or it loops endlessly in a cycle which does not include 1...
beginning with the digit 5.
----
537 = 3 × 179, Mertens function(537) = 0
----
538 = 2 × 269, open meandric number, nontotient; also, the total number of votes in the Electoral College of the United States
----
539 = 72 × 11
----
540 = 22 × 33 × 5, untouchable number, decagonal number
Decagonal number
A decagonal number is a figurate number that represents a decagon. The n-th decagonal number is given by the formulaThe first few decagonal numbers are:...
, Harshad number
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541 is the 100th prime, a lucky prime, a Chen prime and a star number
Star number
A star number is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers is played on.The nth star number is given by the formula 6n + 1...
. Mertens function(541) = 0.
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542 = 2 × 271, nontotient, sum of totient function for first 42 integers
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543 = 3 × 181
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544 = 25 × 17
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545 = 5 × 109, centered square number
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 centered square number equals the number of dots within a...
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546 = 2 × 3 × 7 × 13, sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)
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547 prime number, cuban prime, centered hexagonal number
Centered hexagonal number
A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice....
, centered heptagonal number
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...
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548 = 22 × 137, 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,...
, every positive integer is the sum of at most 548 ninth powers; also the default port for the Apple Filing Protocol
Apple Filing Protocol
The Apple Filing Protocol is a network protocol that offers file services for Mac OS X and original Mac OS. In Mac OS X, AFP is one of several file services supported including Server Message Block , Network File System , File Transfer Protocol , and WebDAV...
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549 = 32 × 61
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550 = 2 × 52 × 11, pentagonal pyramidal number
Pentagonal pyramidal number
A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base. The nth pentagonal pyramidal number is equal to the sum of the first n pentagonal numbers....
, nontotient, Harshad number, also SMTP status code meaning the requested action was not taken because the mailbox is unavailable
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551 = 19 × 29, sum of three consecutive primes (179 + 181 + 191), SMTP status code meaning user is not local
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552 = 23 × 3 × 23, sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103), sum of ten consecutive primes (37 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), pronic number, untouchable number, Harshad number; model number of , SMTP status code meaning requested action aborted because the mailbox is full
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553 = 7 × 79, sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79); model number of , SMTP status code meaning requested action aborted because of faulty mailbox name
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554 = 2 × 277, Mertens function(554) = 6 a record high that stands until 586, nontotient, also SMTP status code meaning transaction failed
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555
555 (number)
555 is the natural number following 554 and preceding 556.- Mathematical properties :It is a sphenic number.In base 10, it is a repdigit, and because it is divisible by the sum of its digits, it is a Harshad number...
is a sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...
, a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
and a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
- The telephone exchange for fictitious phone numbers in US movieFilmA film, also called a movie or motion picture, is a series of still or moving images. It is produced by recording photographic images with cameras, or by creating images using animation techniques or visual effects...
s – see 5-5-5 - The number of keyboard sonatas written by Domenico ScarlattiDomenico ScarlattiGiuseppe Domenico Scarlatti was an Italian composer who spent much of his life in the service of the Portuguese and Spanish royal families. He is classified as a Baroque composer chronologically, although his music was influential in the development of the Classical style...
, according to the catalog by Ralph KirkpatrickRalph KirkpatrickRalph Kirkpatrick was an American musician, musicologist and harpsichordist. He is most famous for his chronological catalog of Domenico Scarlatti's keyboard sonatas.-Life and work:...
. - the model number of the 555 timer IC555 timer ICThe 555 timer IC is an integrated circuit used in a variety of timer, pulse generation and oscillator applications. The part is still in widespread use, thanks to its ease of use, low price and good stability. , it was estimated that 1 billion units are manufactured every year.- Design :The IC...
, a classic integrated circuitIntegrated circuitAn integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...
(chip) implementing a variety of timerTimerA timer is a specialized type of clock. A timer can be used to control the sequence of an event or process. Whereas a stopwatch counts upwards from zero for measuring elapsed time, a timer counts down from a specified time interval, like an hourglass.Timers can be mechanical, electromechanical,...
and multivibratorMultivibratorA multivibrator is an electronic circuit used to implement a variety of simple two-state systems such as oscillators, timers and flip-flops. It is characterized by two amplifying devices cross-coupled by resistors or capacitors...
applications, and historically widely used in electronicsElectronicsElectronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
. - The number of seats of the airlinerAirlinerAn airliner is a large fixed-wing aircraft for transporting passengers and cargo. Such aircraft are operated by airlines. Although the definition of an airliner can vary from country to country, an airliner is typically defined as an aircraft intended for carrying multiple passengers in commercial...
A380-800Airbus A380The Airbus A380 is a double-deck, wide-body, four-engine jet airliner manufactured by the European corporation Airbus, a subsidiary of EADS. It is the largest passenger airliner in the world. Due to its size, many airports had to modify and improve facilities to accommodate it...
.
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556 = 22 × 139, sum of four consecutive primes (131 + 137 + 139 + 149). But it is never the sum of the proper divisors of any integer, making it an untouchable number
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 ....
; happy number; model number of .
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557 prime number, Chen prime, Eisenstein prime with no imaginary part
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558 = 2 × 32 × 31, nontotient, Harshad number. The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993). Also, 558 is in the title of the Star Trek: Deep Space Nine
Star Trek: Deep Space Nine
Star Trek: Deep Space Nine is a science fiction television series set in the Star Trek universe...
episode "The Siege of AR-558
The Siege of AR-558 (DS9 episode)
The Siege of AR-558 is an episode from the seventh season of Star Trek: Deep Space Nine. The number 558 is also the production code of the episode. First aired November 18, 1998. It was written by Ira Steven Behr and Hans Beimler, and directed by Winrich Kolbe...
"
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559 = 13 × 43, sum of five consecutive primes (103 + 107 + 109 + 113 + 127), sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97), nonagonal number, centered cube number
Centered cube number
A centered cube number is a centered figurate number that represents a cube. The centered cube number for n is given byn^3 + ^3.The first few centered cube numbers are...
, model number of
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560 = 24 × 5 × 7, tetrahedral number
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...
, refactorable number
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561 = 3 × 11 × 17, triangular number, hexagonal number
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
, the first Carmichael number
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562 = 2 × 281, Smith number, untouchable number, sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
- 562 is the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.
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563 103rd prime number, safe prime, Wilson prime
Wilson prime
A Wilson prime, named after English mathematician John Wilson, is a prime number p such that p2 divides ! + 1, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides ! + 1.The only known Wilson primes are 5, 13, and...
, Chen prime, Eisenstein prime with no imaginary part, balanced prime, strictly non-palindromic number, sexy prime
Sexy prime
In mathematics, a sexy prime is a prime number that differs from another prime number by six. For example, the numbers 5 and 11 are both sexy primes, because they differ by 6...
, happy number
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564 = 22 × 3 × 47, sum of a twin prime (281 + 283), refactorable number
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565 = 5 × 113, sum of three consecutive primes (181 + 191 + 193), member of the Mian–Chowla sequence, happy number
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566 = 2 × 283, nontotient, happy number
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567 = 34 × 7
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568 = 23 × 71, sum of the first nineteen primes, refactorable number, smallest number whose seventh power is the sum of 7 seventh powers, the room number booked by Benjamin Braddock in the film 1967 film The Graduate
The Graduate
The Graduate is a 1967 American comedy-drama motion picture directed by Mike Nichols. It is based on the 1963 novel The Graduate by Charles Webb, who wrote it shortly after graduating from Williams College. The screenplay was by Buck Henry, who makes a cameo appearance as a hotel clerk, and Calder...
, the name of the Student Union bar at Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
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569 prime number, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number
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570 = 2 × 3 × 5 × 19
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571 prime number, Chen prime, centered triangular number, model number of ]] which appeared in the 2000 movie U-571
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572 = 22 × 11 × 13, nontotient
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573 = 3 × 191, model number of , known as the Konami number
Konami
is a Japanese leading developer and publisher of numerous popular and strong-selling toys, trading cards, anime, tokusatsu, slot machines, arcade cabinets and video games...
because Konami can be represented by 573's Goroawase form of "ko-na-mi".
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574 = 2 × 7 × 41, sphenic number, nontotient
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575 = 52 × 23
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576 = 26 × 32 = 242, sum of four consecutive primes (137 + 139 + 149 + 151), highly totient number
Highly totient number
A highly totient number k is an integer that has more solutions to the equation φ = k, where φ is Euler's totient function, than any integer below it. The first few highly totient numbers are...
, Smith number, untouchable number, Harshad number. 576 is also four-dozen sets of a dozen, which makes it 4 gross.
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577 prime number, Proth prime
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578 = 2 × 172, nontotient
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579 = 3 × 193, a ménage number
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580 = 22 × 5 × 29, sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107)
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581 = 7 × 83, sum of three consecutive primes (191 + 193 + 197)
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582 = 2 × 3 × 97, sphenic number, sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), nontotient
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583 = 11 × 53
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584 = 23 × 73, untouchable number, sum of totient function for first 43 integers, refactorable number
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585 = 32 × 5 × 13
When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".
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586
586 (disambiguation)
586 may mean:* 586 AD, the year* 500 related subjects:** a record Mertens function** the telephone Area code 586 covering in Macomb County, Michigan* The Intel P5 microarchitecture, fifth generation x86 processor architecture, or related subjects:...
= 2 × 293, Mertens function(586) = 7 a record high that stands until 1357; also the number of several popular personal computer processors (such as the Intel)
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587 prime number, safe prime, sum of five consecutive primes (107 + 109 + 113 + 127 + 131), Chen prime, Eisenstein prime with no imaginary part. Outgoing port for email
Email
Electronic mail, commonly known as email or e-mail, is a method of exchanging digital messages from an author to one or more recipients. Modern email operates across the Internet or other computer networks. Some early email systems required that the author and the recipient both be online at the...
message submission
Simple Mail Transfer Protocol
Simple Mail Transfer Protocol is an Internet standard for electronic mail transmission across Internet Protocol networks. SMTP was first defined by RFC 821 , and last updated by RFC 5321 which includes the extended SMTP additions, and is the protocol in widespread use today...
.
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588 = 22 3 × 72, Smith number, Harshad number
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589 = 19 × 31, sum of three consecutive primes (193 + 197 + 199)
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590 = 2 × 5 × 59, sphenic number, nontotient
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591 = 3 × 197
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592 = 24 × 37, Harshad number
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593
593 (number)
593 is the natural number following 592 and preceding 594.-In mathematics:593 is an odd number. It is a prime number, an example of what Paul Erdős and Ernst G. Straus called a Good prime, or a prime whose square is greater than the product of its neighboring two primes. As such it is part of...
prime number, 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...
, sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101), sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), 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, balanced prime, Leyland number, member of the Mian–Chowla sequence, strictly non-palindromic number
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594 = 2 × 33 × 11, sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number
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595 = 5 × 7 × 17, sphenic number, triangular number, centered nonagonal number
Centered nonagonal number
A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers...
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596 = 22 × 149, sum of four consecutive primes (139 + 149 + 151 + 157), nontotient
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597 = 3 × 199
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598 = 2 × 13 × 23 = 51 + 92 + 83, sphenic number
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599 prime number, Chen prime, Eisenstein prime with no imaginary part.