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From Wikipedia, the free encyclopedia

← 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
Quaternary121004
Quinary31005
Senary15046
Octal6208
Duodecimal29412
Hexadecimal19016
Vigesimal10020
Base 36B436
Hebrewת (Tav)

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

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Transcription

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

Integers from 401 to 499

400s

401

A prime number, tetranacci number,[1] 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,[2] Eisenstein prime with no imaginary part, Mertens function returns 0,[3] member of the Mian–Chowla sequence.[4]

402

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

403

403 = 13 × 31, Mertens function returns 0.[3]

404

404 = 22 × 101, Mertens function returns 0,[3] nontotient, noncototient.

405

405 = 34 × 5, Mertens function returns 0,[3] Harshad number;

406

406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number,[5] nontotient

407

407 = 11 × 37,

  • sum of cubes of 4, 0 and 7 (43 + 03 + 73 = 407); narcissistic number[6]
  • sum of three consecutive primes (131 + 137 + 139)
  • Mertens function returns 0[3]
  • 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

409

409 is a prime number, Chen prime,[2] centered triangular number.[10]

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,[12]

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,[3] self number[12]

414

414 = 2 × 32 × 23, Mertens function returns 0,[3] 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

416 = 25 × 13

417

417 = 3 × 139

418

418 = 2 × 11 × 19, sphenic number,

419

A prime number, Sophie Germain prime,[15] Chen prime, Eisenstein prime with no imaginary part, highly cototient number,[16] Mertens function returns 0[3]

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

420s

420

421

422

422 = 2 × 211, Mertens function returns 0,[3] nontotient

423

423 = 32 × 47, Mertens function returns 0,[3] 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,[3] refactorable number,[18] self number[12]

425

425 = 52 × 17, pentagonal number,[19] sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0,[3] 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,

427

427 = 7 × 61, Mertens function returns 0[3]

428

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

429

429 = 3 × 11 × 13, sphenic number, Catalan number[20]

430s

430

430 = 2 × 5 × 43, sphenic number, untouchable number[9]

431

A prime number, Sophie Germain prime,[15] sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), Chen prime, Eisenstein prime with no imaginary part

432

432 = 24 × 33 = 42 × 33, The sum of four consecutive primes (103 + 107 + 109 + 113), a highly totient number,[21] 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 .

433

A prime number, Markov number,[22] star number.[23]

  • 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,[24] self number[12]

436

436 = 22 × 109, nontotient, noncototient

437

437 = 19 × 23

438

438 = 2 × 3 × 73, sphenic number, Smith number.[25]

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[26]

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,[15] 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,[18] Harshad number.

445

445 = 5 × 89

446

446 = 2 × 223, nontotient, self number[12]

447

447 = 3 × 149

448

448 = 26 × 7, untouchable number,[9] refactorable number,[18] 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.[28] 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,[18] Harshad number,

451

451 = 11 × 41; 451 is a Wedderburn–Etherington number[29] and a centered decagonal number;[30] 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

453 = 3 × 151

454

454 = 2 × 227, nontotient, a Smith number[25]

455

455 = 5 × 7 × 13, sphenic number, tetrahedral number[32]

456

456 = 23 × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number[33]

457

  • A prime number, sum of three consecutive primes (149 + 151 + 157), self number.[12]
  • The international standard frequency for radio avalanche transceivers (457 kHz).

458

458 = 2 × 229, nontotient

459

459 = 33 × 17

460s

460

460 = 22 × 5 × 23, centered triangular number,[10] dodecagonal number,[34] 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 , sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number,[35] sparsely totient number[36]

463

A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number,[37]

464

464 = 24 × 29, primitive abundant number[38]

  • 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,[39] Harshad number

466

466 = 2 × 233, noncototient

467

A prime number, safe prime,[40] 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,[18] self number,[12] Harshad number

469

469 = 7 × 67, centered hexagonal number[41]

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[42]

472

472 = 23 × 59, nontotient, untouchable number,[9] refactorable number[18]

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,[9] nonagonal number[43]

475

475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.[4]

476

476 = 22 × 7 × 17, Harshad number

477

477 = 32 × 53, pentagonal number[19]

478

478 = 2 × 239

479

A prime number, safe prime,[40] sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number[12]

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,[21] refactorable number,[18] Harshad number

481

481 = 13 × 37, octagonal number,[8] centered square number,[17] Harshad number

482

482 = 2 × 241, nontotient, noncototient

483

483 = 3 × 7 × 23, sphenic number, Smith number[25]

484

484 = 22 × 112 = 222, nontotient

485

485 = 5 × 97

486

486 = 2 × 35, Harshad number, Perrin number[44]

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.[45]
  • Shorthand for the Intel 80487 floating point processor chip.

488

488 = 23 × 61, nontotient, refactorable number[18]

489

489 = 3 × 163, octahedral number[46]

490s

490

490 = 2 × 5 × 72, noncototient, sum of totient function for first 40 integers, partition number (integer partitions of 19),[47] self number.[12]

491

A prime number, Sophie Germain prime,[15] Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number[26]

492

492 = 22 × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number,[18] 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

495

496

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,[9] admirable number,[48] abundant number

499

A prime number, Chen prime

References

  1. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  2. ^ a b "Sloane's A109611 : Chen primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  3. ^ a b c d e f g h i j k l m n "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  4. ^ a b "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  5. ^ "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  6. ^ "Sloane's A005188 : Armstrong (or Plus Perfect, or narcissistic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  7. ^ "Sloane's A000129 : Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  8. ^ a b "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  9. ^ a b c d e f "Sloane's A005114 : Untouchable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  10. ^ a b "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  11. ^ Google Maps [@googlemaps] (16 June 2016). "117 islands, 150 canals, 409 bridges. Explore #Venice with this #GoogleMaps Trek" (Tweet) – via Twitter.
  12. ^ a b c d e f g h i "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  13. ^ L. Masinter (1 April 1998). "Hyper Text Coffee Pot Control Protocol (HTCPCP/1.0)". Network Working Group (RFC). Retrieved 13 Sep 2018. Any attempt to brew coffee with a teapot should result in the error code "418 I'm a teapot". The resulting entity body MAY be short and stout.
  14. ^ I. Nazar (1 April 2014). "The Hyper Text Coffee Pot Control Protocol for Tea Efflux Appliances (HTCPCP-TEA)" (RFC). ISSN 2070-1721. Retrieved 13 Sep 2018. TEA-capable pots that are not provisioned to brew coffee may return either a status code of 503, indicating temporary unavailability of coffee, or a code of 418 as defined in the base HTCPCP specification to denote a more permanent indication that the pot is a teapot.
  15. ^ a b c d "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  16. ^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  17. ^ a b "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
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  19. ^ a b "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  20. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  21. ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  22. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  23. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  24. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  25. ^ a b c "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  26. ^ a b "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  27. ^ "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  28. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  29. ^ "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  30. ^ "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  31. ^ https://datatracker.ietf.org/doc/draft-ietf-httpbis-legally-restricted-status/
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  33. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  34. ^ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  35. ^ "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  36. ^ "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  37. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  38. ^ "Sloane's A091191 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  39. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  40. ^ a b "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  41. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  42. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  43. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  44. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
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  46. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  47. ^ "Sloane's A000041 : a(n) = number of partitions of n (the partition numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  48. ^ "Sloane's A111592 : Admirable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
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