400 (number)

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 ← 399 400 401 →
Cardinal four hundred
Ordinal 400th
(four hundredth)
Factorization 24× 52
Divisors 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Roman numeral CD
Binary 1100100002
Ternary 1122113
Quaternary 121004
Quinary 31005
Senary 15046
Octal 6208
Duodecimal 29412
Vigesimal 10020
Base 36 B436
Hebrew ת (Tav)

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

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, Mertens function returns 0, member of the Mian–Chowla sequence.

402

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

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.

405

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

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.

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
• 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

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)

413

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

414

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

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 = 25 × 13

417 = 3 × 139

418

418 = 2 × 11 × 19, sphenic 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

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.

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

429

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

430s

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.

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 = 19 × 23

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

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 = 5 × 89

446

446 = 2 × 223, nontotient, self number

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

450s

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.

452

452 = 22 × 113

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

453 = 3 × 151

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

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 = 33 × 17

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

462

462 = 2 × 3 × 7 × 11, binomial coefficient $\tbinom {11}5$, 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,

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.

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

470s

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 = 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

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

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 = 5 × 97

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 200,000,000 that divide their own decimal periods 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

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, 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