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

Mathematical properties

A circle is divided into 400 grads.

Other fields

Four hundred is also

Integers from 401 to 499

400s

401

401 is a prime number, tetranacci number, Chen prime, prime index prime

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, 28th triangular number, centered nonagonal number, even nontotient

407

407 = 11 × 37,

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

415

415 = 5 × 83, logarithmic number

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. It is also the fourth 71-gonal number.

419

A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0

420s

420

421

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.

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

436

436 = 22 × 109, nontotient, noncototient, lazy caterer number

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

441

441 = 32 × 72 = 212

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.

444

444 = 22 × 3 × 37, refactorable number, Harshad number, number of noniamonds without holes, and a repdigit.

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

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

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, stirling number of the second kind , 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).

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

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

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

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

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.

476

476 = 22 × 7 × 17, Harshad number, admirable number

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, largely composite number

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,

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, number of 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

494

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

495

496

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, 4499 - 3499 is prime