400 (number)

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).

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.

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 .

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

Wikisource has original text related to this article:

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.

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

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, which was inspired by the above engine.
HTTP status code for "Conflict"
Green Day have made a song, 409 in Your Coffeemaker, included on their album 1,039/Smoothed Out Slappy Hours.
The area code for a part of eastern Texas.
Bullet For My Valentine has released a song, "Room 409", from the album The Poison

410s

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
415 (group), a rap group from Oakland, 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)

420s

420

Main article: 420 (number)

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

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

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

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.

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

440s

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

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

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 and 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 that author Ray Bradbury understood to be the autoignition point of paper.

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

458

458 = 2 × 229, nontotient

459

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,

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

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

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.

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

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 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.

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 .

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 493 under first definition

494

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

495

Main article: 495 (number)

496

Main article: 496 (number)

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

Integers

0s

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

100s

100 101 102 103 104 105 106 107 108 109

110 111 112 113 114 115 116 117 118 119

120 121 122 123 124 125 126 127 128 129

130 131 132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149

150 151 152 153 154 155 156 157 158 159

160 161 162 163 164 165 166 167 168 169

170 171 172 173 174 175 176 177 178 179

180 181 182 183 184 185 186 187 188 189

190 191 192 193 194 195 196 197 198 199

200s

200 201 202 203 204 205 206 207 208 209

210 211 212 213 214 215 216 217 218 219

220 221 222 223 224 225 226 227 228 229

230 231 232 233 234 235 236 237 238 239

240 241 242 243 244 245 246 247 248 249

250 251 252 253 254 255 256 257 258 259

260 261 262 263 264 265 266 267 268 269

270 271 272 273 274 275 276 277 278 279

280 281 282 283 284 285 286 287 288 289

290 291 292 293 294 295 296 297 298 299

300s

300 301 302 303 304 305 306 307 308 309

310 311 312 313 314 315 316 317 318 319

320 321 322 323 324 325 326 327 328 329

330 331 332 333 334 335 336 337 338 339

340 341 342 343 344 345 346 347 348 349

350 351 352 353 354 355 356 357 358 359

360 361 362 363 364 365 366 367 368 369

370 371 372 373 374 375 376 377 378 379

380 381 382 383 384 385 386 387 388 389

390 391 392 393 394 395 396 397 398 399

400s

400 401 402 403 404 405 406 407 408 409

410 411 412 413 414 415 416 417 418 419

420 421 422 423 424 425 426 427 428 429

430 431 432 433 434 435 436 437 438 439

440 441 442 443 444 445 446 447 448 449

450 451 452 453 454 455 456 457 458 459

460 461 462 463 464 465 466 467 468 469

470 471 472 473 474 475 476 477 478 479

480 481 482 483 484 485 486 487 488 489

490 491 492 493 494 495 496 497 498 499

500s

500 501 502 503 504 505 506 507 508 509

510 511 512 513 514 515 516 517 518 519

520 521 522 523 524 525 526 527 528 529

530 531 532 533 534 535 536 537 538 539

540 541 542 543 544 545 546 547 548 549

550 551 552 553 554 555 556 557 558 559

560 561 562 563 564 565 566 567 568 569

570 571 572 573 574 575 576 577 578 579

580 581 582 583 584 585 586 587 588 589

590 591 592 593 594 595 596 597 598 599

600s

600 601 602 603 604 605 606 607 608 609

610 611 612 613 614 615 616 617 618 619

620 621 622 623 624 625 626 627 628 629

630 631 632 633 634 635 636 637 638 639

640 641 642 643 644 645 646 647 648 649

650 651 652 653 654 655 656 657 658 659

660 661 662 663 664 665 666 667 668 669

670 671 672 673 674 675 676 677 678 679

680 681 682 683 684 685 686 687 688 689

690 691 692 693 694 695 696 697 698 699

700s

700 701 702 703 704 705 706 707 708 709

710 711 712 713 714 715 716 717 718 719

720 721 722 723 724 725 726 727 728 729

730 731 732 733 734 735 736 737 738 739

740 741 742 743 744 745 746 747 748 749

750 751 752 753 754 755 756 757 758 759

760 761 762 763 764 765 766 767 768 769

770 771 772 773 774 775 776 777 778 779

780 781 782 783 784 785 786 787 788 789

790 791 792 793 794 795 796 797 798 799

800s

800 801 802 803 804 805 806 807 808 809

810 811 812 813 814 815 816 817 818 819

820 821 822 823 824 825 826 827 828 829

830 831 832 833 834 835 836 837 838 839

840 841 842 843 844 845 846 847 848 849

850 851 852 853 854 855 856 857 858 859

860 861 862 863 864 865 866 867 868 869

870 871 872 873 874 875 876 877 878 879

880 881 882 883 884 885 886 887 888 889

890 891 892 893 894 895 896 897 898 899

900s

900 901 902 903 904 905 906 907 908 909

910 911 912 913 914 915 916 917 918 919

920 921 922 923 924 925 926 927 928 929

930 931 932 933 934 935 936 937 938 939

940 941 942 943 944 945 946 947 948 949

950 951 952 953 954 955 956 957 958 959

960 961 962 963 964 965 966 967 968 969

970 971 972 973 974 975 976 977 978 979

980 981 982 983 984 985 986 987 988 989

990 991 992 993 994 995 996 997 998 999

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