# 400 (number)

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

## Mathematical properties

A circle is divided into 400 grads.

## Integers from 401 to 499
### 400s
#### 401

401 is a prime number, tetranacci number, Chen prime, prime index prime
* Eisenstein prime with no imaginary part
* 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)
* Mertens function returns 0,
* Member of the Mian–Chowla sequence.

#### 402

402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number, number of graphs with 8 nodes and 9 edges
* HTTP status code for "Payment Required".
* The area code for Nebraska.

#### 403

403 = 13 × 31, heptagonal number, Mertens function returns 0.
* First number that is the product of an emirp pair.
* HTTP 403, the 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 = 2$^2$ × 101, Mertens function returns 0, nontotient, noncototient, number of integer partitions of 20 with an alternating permutation.
* The HTTP 404 status code is usually sent from a web page if a user attempts to reach a broken or dead link. It has since become one of the most commonly reached, and thus most recognizable errors on the World Wide Web.
* Section 404 of the Sarbanes–Oxley Act.
* One of the three area codes of the Atlanta calling area.

#### 405

405 = 3$^4$ × 5, Mertens function returns 0, Harshad number, pentagonal pyramidal number;
* HTTP status code for "Method Not Allowed".
* Area code for central Oklahoma, including Oklahoma City and surrounding suburbs.
* Interstate 405 is a major, heavily traveled freeway in Southern California, known to the local as "The 405".
* Sum of all numbers in a standard (3x3)x(3x3) Sudoku.

#### 406

406 = 2 × 7 × 29, sphenic number, 28th triangular number, centered nonagonal number, even nontotient, Narayana's cow number
* 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.
* Peugeot 406 car.
* Area code for all of Montana.

#### 407

407 = 11 × 37,
* Sum of cubes of 4, 0 and 7 (4$^3$ + 0$^3$ + 7$^3$ = 407); narcissistic number
* Sum of three consecutive primes (131 + 137 + 139)
* Mertens function returns 0
* Harshad number
* Lazy caterer number
* HTTP status code for "Proxy Authentication Required"
* Area code for Orlando, Florida
* Colloquial name for the Express Toll Route in Ontario

#### 408

408 = 2$^3$ × 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 the corner of southeastern 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.

### 410s
#### 410

410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number, number of triangle-free graphs on 8 vertices
* 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)
* The number of possible FM broadcasting frequencies between 87.50 and 108.00 MHz in 50 kHz spacing countries

#### 412

412 = 2$^2$ × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), 412$^{64}$ + 1 is prime
* HTTP status code for "Precondition Failed"
* Area code for Pittsburgh, Pennsylvania.
* Fictitious Police Code for "Overacting" from "St. George and the Dragonet" - Stan Freberg

#### 413

413 = 7 × 59, Mertens function returns 0, self number, Blum integer
* HTTP status code for "Request Entity Too Large"
* Area code for Western Massachusetts.
* An important and recurring number in the webcomic Homestuck by Andrew Hussie.

#### 414

414 = 2 × 3$^2$ × 23, Mertens function returns 0, nontotient, Harshad number, number of balanced partitions of 31
    $\sum _{n=0}^{10}{414}^{n}$ is prime
* 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, logarithmic number
* 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 = 2$^5$ × 13, number of independent vertex sets and vertex covers in the 6-sunlet graph
* 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, Blum integer
* HTTP status code for "Expectation Failed". Also the area code for southwestern Missouri, including Springfield, and Joplin.

#### 418

418 = 2 × 11 × 19; sphenic number, balanced number. It is also the fourth 71-gonal number.
* The sum of the integers between 13 and 31, inclusive.
* The product of its digits as well as the sum of its prime factors are both 32. Also, 131, a strong concatenation of 13 and 31, is the 32nd prime number (while the 32nd composite number is 48).
* The sum of the 84 digits of the 22nd unique prime in decimal (having a very distinct set of digits than all other known terms in the sequence).
* 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)
* The Area Code for Toledo, OH and other surrounding areas.

### 420s
#### 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
* Country calling code for Slovakia

#### 422

422 = 2 × 211, Mertens function returns 0, nontotient, since 422 = 20$^2$ + 20 + 2 it is the maximum number of regions into which 21 intersecting circles divide the plane.

#### 423

423 = 3$^2$ × 47, Mertens function returns 0, Harshad number, number of secondary structures of RNA molecules with 10 nucleotides
* Country calling code for Liechtenstein

#### 424

424 = 2$^3$ × 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 = 5$^2$ × 17, pentagonal number, centered tetrahedral number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0, the second number that can be expressed as the sum of two squares in three different ways (425 = 20$^2$ + 5$^2$ = 19$^2$ + 8$^2$ = 16$^2$ + 13$^2$).
* 425 is an area code in Washington State.

#### 426

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

#### 427

427 = 7 × 61, Mertens function returns 0. 427! + 1 is prime.

#### 428

428 = 2$^2$ × 107, Mertens function returns 0, nontotient, 428$^{32}$ + 1 is prime
* 428: Shibuya Scramble, a video game

#### 429

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

### 430s
#### 430

430 = 2 × 5 × 43, number of primes below 3000, 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, prime index prime, Eisenstein prime with no imaginary part
* It is also the fourth Leyland prime of the second kind.
* Area code 431 is a telephone area code for Manitoba, Canada.

#### 432

432 = 2$^4$ × 3$^3$ = 4$^2$ × 3$^3$, the sum of four consecutive primes (103 + 107 + 109 + 113), a Harshad number, a highly totient number, an Achilles number and the 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 ${\sqrt {432}}$.

#### 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, maximal number of pieces that can be obtained by cutting an annulus with 28 cuts

#### 435

435 = 3 × 5 × 29, sphenic number, 29th triangular number, hexagonal number, self number, number of compositions of 16 into distinct parts
* The number of members in the US House of Representatives.

#### 436

436 = 2$^2$ × 109, nontotient, noncototient, lazy caterer number

#### 437

437 = 19 × 23, Blum integer

#### 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

### 440s
#### 441

441 = 3$^2$ × 7$^2$ = 21$^2$
* 441 is the sum of the cubes of the first 6 natural numbers (441 = 1$^3$ + 2$^3$ + 3$^3$ + 4$^3$ + 5$^3$ + 6$^3$).
* 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 = 21$^2$ + 1, 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 = 2$^2$ × 3 × 37, refactorable number, Harshad number, number of noniamonds without holes, and a repdigit.
* The title of the final track of Autechre's 1993 debut album Incunabula.
* The 444th Fighter Squadron "Spare", a fictional air squadron in Ace Combat 7: Skies Unknown.

#### 445

445 = 5 × 89, number of series-reduced trees with 17 nodes

#### 446

446 = 2 × 223, nontotient, self number

#### 447

447 = 3 × 149, number of 1's in all partitions of 22 into odd parts
* The flight number of Air France Flight 447

#### 448

448 = 2$^6$ × 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 10$^{1000}$

### 450s
#### 450

450 = 2 × 3$^2$ × 5$^2$, 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.
** By extension, the numbers "451" are often included as the first security code a player encounters in Immersive sim video games as a reference to the System Shock series of games which first included the code as their own reference to Bradbury's novel.
* 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 = 2$^2$ × 113, number of surface-points of a tetrahedron with edge-length 15
* SMTP code meaning that the requested mail action was not carried out because of insufficient system storage

#### 453

453 = 3 × 151, Blum integer

#### 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.
* The sum of the squares of the first 455 primes is divisible by 455.

#### 456

456 = 2$^3$ × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number, icosahedral number
* In the TV show Torchwood: Children of Earth, the antagonists were an alien species with the designation 456.
* One of the two values of the magical formula, IPSOS, the other being 696.
* Number of contestants in the South Korean Netflix drama Squid Game.

#### 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, number of partitions of 24 into divisors of 24

#### 459

459 = 3$^3$ × 17, triangular matchstick number
* 459 West 18th Street, a residential building at that address in Manhattan's West Chelsea neighborhood, built in 2008.

### 460s
#### 460

460 = 2$^2$ × 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, prime index prime

#### 462

462 = 2 × 3 × 7 × 11, binomial coefficient ${\tbinom {11}{5}}$, stirling number of the second kind $\left\{{9 \atop 7}\right\}$, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number, sparsely totient number, idoneal number

#### 463

A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number. This number is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503).
* 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 = 2$^4$ × 29, primitive abundant number, since 464 = 21$^2$ + 21 + 2 it is the maximum number of regions into which 22 intersecting circles divide the plane, maximal number of pieces that can be obtained by cutting an annulus with 29 cuts
* In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase.
* Model number of the home computer Amstrad CPC 464.

#### 465

465 = 3 × 5 × 31, sphenic number, 30th triangular number, member of the Padovan sequence, Harshad number

#### 466

466 = 2 × 233, noncototient, lazy caterer number.

#### 467

A prime number, safe prime, sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part
    $\sum _{n=0}^{10}{467}^{n}$ is prime

#### 468

468 = 2$^2$ × 3$^2$ × 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. 469! - 1 is prime.

### 470s
#### 470

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient, cake number
* 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, φ(471) = φ(σ(471)).

#### 472

472 = 2$^3$ × 59, nontotient, untouchable number, refactorable number, number of distinct ways to cut a 5 × 5 square into squares with integer sides
* The Amstrad CPC472 was a short-lived home computer for the Spanish market.

#### 473

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

#### 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 = 5$^2$ × 19, 49-gonal number, member of the Mian–Chowla sequence.

#### 476

476 = 2$^2$ × 7 × 17, Harshad number, admirable number

#### 477

477 = 3$^2$ × 53, pentagonal number

#### 478

478 = 2 × 239, Companion Pell number, number of partitions of 26 that do not contain 1 as a part

#### 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.

### 480s
#### 480

480 = 2$^5$ × 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, largely composite number
    $\sum _{n=0}^{10}{480}^{n}$ is prime

#### 481

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

#### 482

482 = 2 × 241, nontotient, noncototient, number of series-reduced planted trees with 15 nodes

#### 483

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

#### 484

484 = 2$^2$ × 11$^2$ = 22$^2$, palindromic square, nontotient

#### 485

485 = 5 × 97, number of triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions
* RS-485

#### 486

486 = 2 × 3$^5$, 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 7.74 × 10$^{13}$ that divide their own decimal repetends are 3, 487, and 56598313.
* Shorthand for the Intel 80487 floating point processor chip.

#### 488

488 = 2$^3$ × 61, nontotient, refactorable number, φ(488) = φ(σ(488)), number of surface points on a cube with edge-length 10.

#### 489

489 = 3 × 163, octahedral number

### 490s
#### 490

490 = 2 × 5 × 7$^2$, noncototient, sum of totient function for first 40 integers, number of integer partitions of 19, self number.
* A (possibly arbitrary) large number in the Christian Gospel of Matthew. In Matthew 18:21–35, Jesus tells the Parable of the Unforgiving Servant, instructing Peter to forgive his brother "seventy times seven" times when his brother sins against him .

#### 491

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

#### 492

492 = 2$^2$ × 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, the 493d centered octagonal number is also a centered square number

#### 494

494 = 2 × 13 × 19 = $\left\langle \!\!\left\langle {8 \atop 1}\right\rangle \!\!\right\rangle$, sphenic number, nontotient

#### 497

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

#### 498

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

#### 499

A prime number, isolated prime, Chen prime, 4$^{499}$ - 3$^{499}$ is prime