# 400 (number)

(Redirected from 414 (number))

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

 ← 399 400 401 →
Cardinalfour hundred
Ordinal400th
(four hundredth)
Factorization24 × 52
Divisors1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Greek numeralΥ´
Roman numeralCD
Binary1100100002
Ternary1122113
Senary15046
Octal6208
Duodecimal29412
Hebrewת (Tav)

## 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

## Integers from 401 to 499

### 400s

#### 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, prime index prime, 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

#### 403

403 = 13 × 31, heptagonal number, Mertens function returns 0.

#### 404

404 = 22 × 101, Mertens function returns 0, nontotient, noncototient, number of integer partitions of 20 with an alternating permutation.

#### 405

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

#### 406

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

• 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 (43 + 03 + 73 = 407); narcissistic number
• sum of three consecutive primes (131 + 137 + 139)
• Mertens function returns 0
• lazy caterer number (sequence A000124 in the OEIS)
• 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

#### 409

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

### 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

#### 411

411 = 3 × 137, self number,

#### 412

412 = 22 × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), 41264 + 1 is prime

#### 413

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

#### 414

414 = 2 × 32 × 23, Mertens function returns 0, nontotient, Harshad number, number of balanced partitions of 31

$\sum _{n=0}^{10}{414}^{n}$  is prime

#### 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 = 25 × 13, number of independent vertex sets and vertex covers in the 6-sunlet graph

#### 417

417 = 3 × 139, Blum integer

#### 418

418 = 2 × 11 × 19, sphenic number, balanced number

#### 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)

### 420s

#### 420

420 = 22 × 3 × 5 × 7

#### 422

422 = 2 × 211, Mertens function returns 0, nontotient, since 422 = 202 + 20 + 2 it is the maximum number of regions into which 21 intersecting circles divide the plane.

#### 423

423 = 32 × 47, Mertens function returns 0, Harshad number, number of secondary structures of RNA molecules with 10 nucleotides

#### 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, 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 = 202 + 52 = 192 + 82 = 162 + 132).

#### 426

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

#### 427

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

#### 428

428 = 22 × 107, Mertens function returns 0, nontotient, 42832 + 1 is prime

#### 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

#### 432

432 = 24 × 33 = 42 × 33, 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, triangular number, hexagonal number, self number, number of compositions of 16 into distinct parts

#### 436

436 = 22 × 109, nontotient, noncototient, lazy caterer number (sequence A000124 in the OEIS)

#### 437

437 = 19 × 23, Blum integer

#### 438

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

#### 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

#### 440

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

#### 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 = 212 + 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 = 22 × 3 × 37, refactorable number, Harshad number, number of noniamonds without holes.

#### 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

#### 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

### 450s

#### 450

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

#### 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.

#### 452

452 = 22 × 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

#### 456

456 = 23 × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number, icosahedral 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, number of partitions of 24 into divisors of 24

#### 459

459 = 33 × 17, triangular matchstick number

### 460s

#### 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, 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,

#### 464

464 = 24 × 29, primitive abundant number, since 464 = 212 + 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, triangular number, member of the Padovan sequence, Harshad number

#### 466

466 = 2 × 233, noncototient, lazy caterer number (sequence A000124 in the OEIS)

#### 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 = 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. 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 = 23 × 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 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.

#### 477

477 = 32 × 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

### 480s

#### 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

$\sum _{n=0}^{10}{480}^{n}$  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 = 22 × 112 = 222, palindromic square, nontotient

#### 485

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

#### 486

486 = 2 × 35, Harshad number, Perrin number

#### 487

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

• The only primes under 7.74 × 1013 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, 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 × 72, noncototient, sum of totient function for first 40 integers, partition number (integer partitions of 19), self number.

#### 491

A prime number, isolated prime, 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, the 493d centered octagonal number is also a centered square number

#### 495

495 = 32 × 5 × 11, pentatope number

#### 496

496 = 24 × 31. It 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), lazy caterer number (sequence A000124 in the OEIS)

#### 498

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

#### 499

A prime number, isolated prime, Chen prime, 4499 - 3499 is prime