 500 (number)

For other uses, see 500 (disambiguation).
500 Cardinal 500
five hundredOrdinal 500th
(five hundredth)Factorization Roman numeral D Binary 111110100_{2} Octal 764_{8} Duodecimal 358_{12} Hexadecimal 1F4_{16} 500 (five hundred) is the natural number following 499 and preceding 501.
Contents
Mathematical properties
500 is a Harshad number.
Other fields
Five hundred is also
 many NASCAR races often use the number 500 at the end of their race names (i.e. Daytona 500), to denote the length of the race (in miles, kilometers or laps).
 the longest advertised distance of the IndyCar Series and its premier race, the Indianapolis 500.
 an Italian car, the Fiat 500, or a number of cars in the United States built by Ford: the Ford Five Hundred, Galaxie 500 and Custom 500.
 a name of two different card games, see 500 (card game) for the trick taking game and 500 Rum for the rummy game.
 (500) Days of Summer is a 2009 film directed by Marc Webb
 an outdoor ball/disc game, see 500 (outdoor game)
 an HTTP status code for Internal Server Error
 an SMTP status code meaning a syntax error has occurred due to unrecognized command
 the years AD 500, 500 BC.
 the winning permillage of a sports team with equal numbers of wins and losses. Such teams are often referred to as "500 teams".
Slang names
 Monkey (UK slang for £500; USA slang for $500)^{[1]}
Numbers from 501 to 599
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 timeout, SMTP status code meaning bad sequence of commands
504 = 2^{3} × 3^{2} × 7, tribonacci number, semimeandric 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 U505
This number is the magic constant of n×n normal magic square and nqueens problem for n = 10.
New Mexico – Before October 7, 2007, The United States state of New Mexico had a single area code^{[2]} 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 × 13^{2}
508 = 2^{2} × 127, sum of four consecutive primes (113 + 127 + 131 + 137)
509 prime number, Sophie Germain prime, smallest Sophie Germain prime to start a 4term 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:
 511, a roadway status and transit information hotline in many metropolitan areas of the United States.
 Paul Erdős had 511 collaborators.
512 = 2^{9}, power of two, cube of 8, Leyland number, Dudeney number, Harshad number
513 = 3^{3} × 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 = 2^{2} × 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 = 5^{1} + 1^{2} + 8^{3} (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 = 2^{3} × 5 × 13, untouchable number
521 Lucas prime, Chen prime, Eisenstein prime with no imaginary part
522 = 2 × 3^{2} × 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 = 2^{2} × 131
525 = 3 × 5^{2} × 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 groups)
528 = 2^{4} × 3 × 11, triangular number
529 = 23^{2}, centered octagonal number, also Section 529 of the IRS tax code organizes 529 plans 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 = 3^{2} × 59, Harshad number
532 = 2^{2} × 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, 34n^{3} + 51n^{2} + 27n + 5 for n = 2; this polynomial plays an essential role in Apéry's proof that ζ(3) 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.^{[3]}
536 = 2^{3} × 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 = 7^{2} × 11
540 = 2^{2} × 3^{3} × 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 = 2^{5} × 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 = 2^{2} × 137, nontotient, every positive integer is the sum of at most 548 ninth powers; also the default port for the Apple Filing Protocol
549 = 3^{2} × 61
550 = 2 × 5^{2} × 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 = 2^{3} × 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 U552, 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 U553, 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
 The telephone exchange for fictitious phone numbers in US movies – see 555
 The number of keyboard sonatas written by Domenico Scarlatti, according to the catalog by Ralph Kirkpatrick.
 the model number of the 555 timer IC, a classic integrated circuit (chip) implementing a variety of timer and multivibrator applications, and historically widely used in electronics.
 The number of seats of the airliner A380800.
556 = 2^{2} × 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 U556.
557 prime number, Chen prime, Eisenstein prime with no imaginary part
558 = 2 × 3^{2} × 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 AR558"
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 U559
560 = 2^{4} × 5 × 7, tetrahedral number, refactorable number
561 = 3 × 11 × 17, triangular number, hexagonal number, the first Carmichael number^{[4]}
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.
563 103rd prime number, safe prime, Wilson prime, Chen prime, Eisenstein prime with no imaginary part, balanced prime, strictly nonpalindromic number, sexy prime, happy number
564 = 2^{2} × 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 = 3^{4} × 7
568 = 2^{3} × 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 nonpalindromic number
570 = 2 × 3 × 5 × 19
571 prime number, Chen prime, centered triangular number, model number of U571]] which appeared in the 2000 movie U571
572 = 2^{2} × 11 × 13, nontotient
573 = 3 × 191, model number of German submarine U573, known as the Konami number because Konami can be represented by 573's Goroawase form of "konami".
574 = 2 × 7 × 41, sphenic number, nontotient
575 = 5^{2} × 23
576 = 2^{6} × 3^{2} = 24^{2}, sum of four consecutive primes (137 + 139 + 149 + 151), highly totient number, Smith number, untouchable number, Harshad number. 576 is also fourdozen sets of a dozen, which makes it 4 gross.
577 prime number, Proth prime
578 = 2 × 17^{2}, nontotient
579 = 3 × 193, a ménage number
580 = 2^{2} × 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 = 2^{3} × 73, untouchable number, sum of totient function for first 43 integers, refactorable number
585 = 3^{2} × 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 = 2^{2} 3 × 7^{2}, 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 = 2^{4} × 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 nonpalindromic number
594 = 2 × 3^{3} × 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 = 2^{2} × 149, sum of four consecutive primes (139 + 149 + 151 + 157), nontotient
597 = 3 × 199
598 = 2 × 13 × 23 = 5^{1} + 9^{2} + 8^{3}, sphenic number
599 prime number, Chen prime, Eisenstein prime with no imaginary part.
References
 ^ Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0304340049
 ^ 'Verizon Area Code For New Mexico' http://support.vzw.com/pdf/newmexico_split_map.pdf
 ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. http://www.nytimes.com/2011/10/30/magazine/thedangerouspoliticsofinternethumorinchina.html. Retrieved November 1, 2011.
 ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 9781848000001.
Categories: Integers
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