Samiksha Jaiswal (Editor)

400 (number)

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400
  
401 →

Ordinal
  
400th (four hundredth)

Roman numeral
  
CD

Cardinal
  
four hundred

Factorization
  
2× 5

Divisors
  
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

400 (four hundred) is the natural number following 399 and preceding 401.

Contents

Mathematical properties

400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111).

A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units).

400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number.

Other fields

Four hundred is also

  • The Four Hundred (oligarchy) of ancient Athens.
  • an HTTP status code for a bad client request.
  • The Four Hundred (sometimes The Four Hundred Club) a phrase meaning the wealthiest, most famous, or most powerful social group (see, e.g., Ward McAllister), leading to the generation of such lists as the Forbes 400
  • The Atari 400 home computer.
  • A former limited stop bus route which operated from Bolton to Stockport and Manchester Airport from 1970 to 2004, known as the Trans-Lancs Express.
  • in the title of the film Les Quatre Cent Coups (The 400 Blows), a French film directed by François Truffaut.
  • A Lebanese card game. 400 (card game)
  • the designation for a class of Ontario highways called 400-Series Highways.
  • The 400, later the Twin Cities 400, a Chicago and North Western Railway passenger train that traveled 400 miles between Minneapolis/St. Paul and Chicago, Illinois in 400 minutes.
  • The yard number of the RMS Olympic, the RMS Titanic's sister ship.
  • .400 (2 hits out of 5 at-bats) is a numerically significant annual batting average statistic in Major League Baseball, last accomplished by Ted Williams of the Boston Red Sox in 1941.
  • The number of days in a Gregorian calendar year changes according to a cycle of exactly 400 years, of which 97 are leap years and 303 are common.
  • The Intertestamental period or period of time between the writings of the Hebrew Bible and the Christian New Testament texts is traditionally considered to be a roughly four hundred-year period
  • The Sun is approximately 400 times the size of the Moon but also is approximately 400 times further away, creating the temporary illusion in which the Sun and Moon in Earth's sky appear as if of similar size.
  • In gematria 400 is the largest single number that can be represented without using the Sophit forms (see Kaph, Mem, Nun, Pe, and Tzade).

    • 401

    A prime number, tetranacci number, sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71), sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Chen prime, Eisenstein prime with no imaginary part, Mertens function returns 0, member of the Mian–Chowla sequence.

  • HTTP status code for "Unauthorized", area code for Rhode Island, also in the name of a retirement plan, 401(k). Stephen Colbert's Formula 401, a "man seed" based product brand his persona on The Colbert Report promotes for sale to the public [1].
  • Ontario Highway 401, colloquially referred to as the four-oh-one, is a popular Canadian highway 817.9 kilometres (508.2 mi) that stretches from Windsor to the Quebec border, passing through Toronto. It turns into Quebec Autoroute 20 at the Quebec/Ontario border which leads to the cities of Montreal and Quebec.

    • 402

    402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number,

  • HTTP status code for "Payment Required", area code for Nebraska

    • 403

    403 = 13 × 31, Mertens function returns 0.

  • HTTP status code for "Forbidden"
  • Also in the name of a retirement plan in the United States, 403(b).
  • The area code for southern Alberta.

    • 404

    404 = 22 × 101, Mertens function returns 0, nontotient, noncototient.

  • HTTP status code for "Not Found", perhaps the most famous HTTP status code.
  • Section 404 of the Sarbanes–Oxley Act.
  • One of the three area codes of the Atlanta calling area.

    • 405

    405 = 34 × 5, Mertens function returns 0, Harshad number;

  • HTTP status code for "Method Not Allowed".
  • Area code for central Oklahoma, including Oklahoma City and surrounding suburbs.

    • 406

    406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient

  • HTTP status code for "Not Acceptable".
  • 406 is a poem by John Boyle O'Reilly. It was believed to have been the number of one of O'Reilly's prison cells, and was the number of his first hotel room after he arrived in the United States. Hence the number had a mystical significance to him, as intimated in the poem.
  • See also the Peugeot 406 car.
  • Area code for all of Montana.

    • 407

    407 = 11 × 37,

  • sum of cubes of 4, 0 and 7 (43 + 03 + 73 = 407); narcissistic number
  • sum of three consecutive primes (131 + 137 + 139)
  • Mertens function returns 0
  • Harshad number
  • HTTP status code for "Proxy Authentication Required"
  • Area code for Orlando, Florida
  • Colloquial name for the Express Toll Route in Ontario

    • 408

    408 = 23 × 3 × 17

  • Sum of four consecutive primes (97 + 101 + 103 + 107)
  • Sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67)
  • Pell number
  • Mertens function returns 0
  • Octagonal number
  • Untouchable number
  • Harshad number
  • HTTP status code for "Request Timeout"
  • Area code for the Silicon Valley

    • 409

    409 is a prime number, Chen prime, centered triangular number.

  • A family of cleaning products, Formula 409
  • An engine known as the Chevrolet 409, a 409 cubic inch W-series V8.
  • The song "409" by The Beach Boys, inspired by the above engine
  • HTTP status code for "Conflict"
  • A Green Day song, 409 in Your Coffeemaker, included on their album 1,039/Smoothed Out Slappy Hours
  • The area code for a part of eastern Texas
  • Venice has 409 bridges.
  • A Bullet For My Valentine song, "Room 409", from the album The Poison
  • Joe Paterno holds the record as the winningest head coach in NCAA FBS with 409 victories.

    • 410

    410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number

  • HTTP status code for "Gone".
  • Area Code 410, a telephone area code for the US State of Maryland, representing portions of the state including the Baltimore metropolitan area and the Eastern Shore.

    • 411

    411 = 3 × 137, self number,

  • HTTP status code for "Length Required", slang for information (see 4-1-1)

    • 412

    412 = 22 × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)

  • HTTP status code for "Precondition Failed"
  • Area code for Pittsburgh, Pennsylvania.
  • Fictitious Police Code for "Overacting" from "St. George and the Dragonet" - Stan Freeberg

    • 413

    413 = 7 × 59, Mertens function returns 0, self number

  • HTTP status code for "Request Entity Too Large", area code for Western Massachusetts.

    • 414

    414 = 2 × 32 × 23, Mertens function returns 0, nontotient, Harshad number

  • HTTP status code for "Request-URI Too Long"
  • Area code for Milwaukee, Wisconsin.
  • The 414s, a group of hackers from Milwaukee, Wisconsin.

    • 415

    415 = 5 × 83,

  • HTTP status code for "Unsupported Media Type"
  • 415 Records, a record label
  • 415 refers to California Penal Code, section 415, pertaining to public fighting, public disturbance, and public use of offensive words likely to provoke an immediate violent reaction.
  • Area code 415, a telephone area code for San Francisco, California

    • 416

    416 = 25 × 13

  • HTTP status code for "Requested Range Not Satisfiable"
  • 416 is also a nickname for the city of Toronto, based on the area code it used before overlay plans added two more area codes.

    • 417

    417 = 3 × 139

  • HTTP status code for "Expectation Failed". Also the area code for southwestern Missouri, including Springfield, and Joplin.

    • 418

    418 = 2 × 11 × 19, sphenic number,

  • the number of Abrahadabra
  • Hyper Text Coffee Pot Control Protocol status code for "Teapot" as an April Fools' joke.

    • 419

    A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0

  • refers to the Nigerian advance fee fraud scheme (after the section of the Nigerian Criminal Code it violates)

    • 421

    A prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97), centered square number, also SMTP code meaning the transmission channel will be closing

    422

    422 = 2 × 211, Mertens function returns 0, nontotient

    423

    423 = 32 × 47, Mertens function returns 0, Harshad number

    424

    424 = 23 × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, refactorable number, self number

    425

    425 = 52 × 17, pentagonal number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0.

  • 425 is an area code in Washington State.

    • 426

    426 = 2 × 3 × 71, sphenic number, nontotient,

    427

    427 = 7 × 61, Mertens function returns 0

  • 427 is the room number for the protagonist, Stanley, in "The Stanley Parable"

    • 428

    428 = 22 × 107, Mertens function returns 0, nontotient

  • 428: Fūsa Sareta Shibuya de, a video game

    • 429

    429 = 3 × 11 × 13, sphenic number, Catalan number

    430

    430 = 2 × 5 × 43, sphenic number, untouchable number

    431

    A prime number, Sophie Germain prime, sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), Chen prime, Eisenstein prime with no imaginary part

  • The distance between Earth and the star Polaris in light years
  • Area code 431 is a telephone area code for Manitoba, Canada.

    • 432

    432 = 24 x 33 = 42 x 33, The sum of four consecutive primes (103 + 107 + 109 + 113), a highly totient number, sum of totient function for first 37 integers. 432! is the first factorial that is not a Harshad number in base 10. 432 is also three-dozen sets of a dozen, making it three gross. An equilateral triangle whose area and perimeter are equal, has an area (and perimeter) equal to 432 .

    433

    A prime number, Markov number, star number.

  • The perfect score in the game show Fifteen To One, only ever achieved once in over 2000 shows.
  • 433 can refer to composer John Cage's composition 4′33″ (pronounced "Four minutes, thirty-three seconds" or just "Four thirty-three").

    • 434

    434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83), nontotient

    435

    435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number, self number

    436

    436 = 22 × 109, nontotient, noncototient

    437

    437 = 19 × 23

    438

    438 = 2 × 3 × 73, sphenic number, Smith number.

  • The "438 match" or "438 game" has been used by cricket media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

    • 439

    A prime number, sum of three consecutive primes (139 + 149 + 151), sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), strictly non-palindromic number

    440

    440 = 23 × 5 × 11, the sum of the first seventeen prime numbers, Harshad number,

  • in hertz, the standard frequency to which most orchestras tune the pitch A above middle C. A few orchestras tune slightly flatter or sharper than this.

    • 441

    441 = 32 × 72 = 212

  • 441 is the sum of the cubes of the first 6 natural numbers (441 = 13 + 23 + 33 + 43 + 53 + 63).
  • 441 is a centered octagonal number, a refactorable number, and a Harshad number.
  • 441 is the number of squares on a Super Scrabble board.

    • 442

    442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)

    443

    A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659.

  • In computing, it is the default port for HTTPS connections.

    • 444

    444 = 22 × 3 × 37, refactorable number, Harshad number.

    445

    445 = 5 × 89

    446

    446 = 2 × 223, nontotient, self number

    447

    447 = 3 × 149

    448

    448 = 26 × 7, untouchable number, refactorable number, Harshad number

    449

    A prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101), Chen prime, Eisenstein prime with no imaginary part, Proth prime. Also the largest number whose factorial is less than 101000

    450

    450 = 2 × 32 × 52, nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number,

  • SMTP code meaning the requested mail action was not carried out.
  • A perfect score in Canadian five-pin bowling.
  • An area code in Southern Quebec.

    • 451

    451 = 11 × 41; 451 is a Wedderburn–Etherington number and a centered decagonal number; its reciprocal has period 10; 451 is the smallest number with this period reciprocal length.

  • The novel Fahrenheit 451 refers to the temperature in Fahrenheit that author Ray Bradbury understood to be the autoignition point of paper.
  • HTTP status code for "Unavailable For Legal Reasons" a HTTP response error when the user requests an illegal resource, such as a web page censored by a government.

    • 452

    452 = 22 × 113

  • SMTP code meaning that the requested mail action was not carried out because of insufficient system storage

    • 453

    453 = 3 × 151

    454

    454 = 2 × 227, nontotient, a Smith number

    455

    455 = 5 × 7 × 13, sphenic number, tetrahedral number

  • 455 Rocket is the title of a song by Kathy Mattea
  • 455 kHz is a standard intermediate frequency for analog superheterodyne AM broadcast band receivers.

    • 456

    456 = 23 × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number

    457

  • A prime number, sum of three consecutive primes (149 + 151 + 157), self number.
  • The international standard frequency for radio avalanche transceivers (457 kHz).

    • 458

    458 = 2 × 229, nontotient

    459

    459 = 33 × 17

  • 459 West 18th Street, a residential building at that address in Manhattan's West Chelsea neighborhood, built io 2008.

    • 460

    460 = 22 × 5 × 23, centered triangular number, dodecagonal number, Harshad number, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)

    461

    A prime number, Chen prime, sexy prime with 467, Eisenstein prime with no imaginary part

    462

    462 = 2 × 3 × 7 × 11, binomial coefficient ( 11 5 ) , sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number, sparsely totient number

    463

    A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number,

  • Number of days in the synodic period of Ceres
  • A common baseball double play (see baseball positions)
  • A single by Buck 65, named after the baseball term

    • 464

    464 = 24 × 29, primitive abundant number

  • In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase.
  • See also: 4-6-4, the year AD 464.

    • 465

    465 = 3 × 5 × 31, sphenic number, triangular number, member of the Padovan sequence, Harshad number

    466

    466 = 2 × 233, noncototient

    467

    A prime number, safe prime, sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part

    468

    468 = 22 × 32 × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number, self number, Harshad number

    469

    469 = 7 × 67, centered hexagonal number

    470

    470 = 2 × 5 × 47, sphenic number, nontotient, noncototient

  • In golf, 470 is the minimum length in yards from the tee to the hole on a Par 5.
  • 470 is an Olympic class of sailing dinghy

    • 471

    471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number

    472

    472 = 23 × 59, nontotient, untouchable number, refactorable number

    473

    473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103)

    474

    474 = 2 × 3 × 79, sphenic number, sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), nontotient, noncototient, sum of totient function for first 39 integers, untouchable number, nonagonal number

    475

    475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.

    476

    476 = 22 × 7 × 17, Harshad number

    477

    477 = 32 × 53, pentagonal number

    478

    478 = 2 × 239

    479

    A prime number, safe prime, sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number

  • Also an area code in the U.S. state of Arkansas.

    • 480

    480 = 25 × 3 × 5, sum of a twin prime (239 + 241), sum of four consecutive primes (109 + 113 + 127 + 131), highly totient number, refactorable number, Harshad number

    481

    481 = 13 × 37, octagonal number, centered square number, Harshad number

    482

    482 = 2 × 241, nontotient, noncototient

    483

    483 = 3 × 7 × 23, sphenic number, Smith number

    484

    484 = 22 × 112 = 222, nontotient

    485

    485 = 5 × 97

    486

    486 = 2 × 35, Harshad number, Perrin number

  • Shorthand for the Intel 80486 microprocessor chip.

    • 487

    A prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime,

  • The only primes under 200,000,000 that divide their own decimal repetends are 3, 487, and 56598313.
  • Shorthand for the Intel 80487 floating point processor chip.

    • 488

    488 = 23 × 61, nontotient, refactorable number

    489

    489 = 3 × 163, octahedral number

    490

    490 = 2 × 5 × 72, noncototient, sum of totient function for first 40 integers, partition number (integer partitions of 19), self number.

  • In Christianity, the Gospel of Matthew (Matthew 18:21-22) says that Jesus told Peter to forgive his brother "seventy times seven" times when his brother sins against him [2].

    • 491

    A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number

    492

    492 = 22 × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number, member of a Ruth–Aaron pair with 493 under first definition

    493

    493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 492 under first definition

    494

    494 = 2 × 13 × 19, sphenic number, nontotient

    496

    is the third perfect number, a number whose divisors add up to the actual number (1+2+4+8+16+31+62+124+248=496)

    497

    497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107)

    498

    498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number

    499

    A prime number, Chen prime

    References

    400 (number) Wikipedia
    (Text) CC BY-SA