Overview
400 (four hundred) is the natural number following 399 and preceding 401.
Mathematical properties
A circle is divided into 400 grads.
401
401 is a prime number, a Chen prime, a prime index prime, an Eisenstein prime with no imaginary part, a tetranacci number, a zero of Mertens function, and a member of the Mian–Chowla sequence. It is the sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71) and the sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).
402
402 = 2 × 3 × 67. It is a sphenic number, a nontotient and a Harshad number. There are 402 graphs with 8 nodes and 9 edges.
403
403 = 13 × 31. It is a heptagonal number, a zero of Mertens function,
404
404 = 2 2 × 101, a zero of Mertens function, The HTTP 404 status code is usually sent from a web page if a user attempts to reach a broken or dead link. It has since become one of the most commonly reached, and thus most recognizable errors on the World Wide Web.
405
405 = 3 4 × 5. It is a zero of Mertens function, a Harshad number and a pentagonal pyramidal number.
406
406 = 2 × 7 × 29. It is a sphenic number, the 28th triangular number, a centered nonagonal number, an even nontotient, and a Narayana's cow number. 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. It is a zero of Mertens function, It is the sum of the cubes of 4, 0 and 7 (4 3 + 0 3 + 7 3 = 407) and thus a narcissistic number. It is the sum of three consecutive primes (131 + 137 + 139).
408
408 = 2 3 × 3 × 17. It is a Pell number, a zero of Mertens function, an Untouchable number and a Harshad number. It is the sum of four consecutive primes (97 + 101 + 103 + 107) and the sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
409
409 is a prime number, a Chen prime,
410
410 = 2 × 5 × 41. It is a sphenic number, a nontotient, a Harshad number, and the sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79). There are 410 triangle-free graphs on 8 vertices.
411
411 = 3 × 137. It is a self number.
412
412 = 2 2 × 103. It is a nontotient, a noncototient, and the sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59). 412 64 + 1 is prime
413
413 = 7 × 59. It is a zero of Mertens function, a self number, and a Blum integer.
414
414 = 2 × 3 2 × 23. It is a zero of Mertens function, : \sum_ n=0 ^ 10 414 ^ n is prime
415
415 = 5 × 83. It is a logarithmic number.
416
416 = 2 5 × 13. There are independent vertex sets and vertex covers in the 6-sunlet graph
417
417 = 3 × 139. It is a Blum integer.
418
418 = 2 × 11 × 19. It is a sphenic number, a balanced number. and the fourth 71-gonal number. It is the sum of the integers between 13 and 31, inclusive. The sum of the 84 digits of the 22nd unique prime in decimal (having a very distinct set of digits than all other known terms in the sequence).
419
419 is a prime number, a Sophie Germain prime, a Chen prime, and a zero of Mertens function.
421
421 is a prime number, a centered square number, and the sum of five consecutive primes (73 + 79 + 83 + 89 + 97).
422
422 = 2 × 211. It is a zero of Mertens function
423
423 = 3 2 × 47. It is a zero of Mertens function
424
424 = 2 3 × 53. It is a zero of Mertens function, a self number and the sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).
425
425 = 5 2 × 17. It is a pentagonal number, a centered tetrahedral number, a zero of Mertens function, and the sum of three consecutive primes (137 + 139 + 149). It is the second number that can be expressed as the sum of two squares in three different ways (425 = 20 2 + 5 2 = 19 2 + 8 2 = 16 2 + 13 2 ).
426
426 = 2 × 3 × 71. It is a sphenic number, a nontotient, and an untouchable number.
427
427 = 7 × 61. It is a zero of Mertens function. 427! + 1 is prime.
428
428 = 2 2 × 107. It is a zero of Mertens function and a nontotient. 428 32 + 1 is prime
429
429 = 3 × 11 × 13. It is a sphenic number and a Catalan number.
430
430 = 2 × 5 × 43. It is a sphenic number and an untouchable number.
431
431 is a prime number, a Sophie Germain prime, a Chen prime, a prime index prime, an Eisenstein prime with no imaginary part, the fourth Leyland prime of the second kind and the sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73).
432
432 = 2 4 × 3 3 = 4 2 × 3 3 . It is a Harshad number, a highly totient number, an Achilles number and the sum of the totient function for first 37 integers. It is the sum of four consecutive primes (103 + 107 + 109 + 113). 432! is the first factorial that is not a Harshad number in base 10. An equilateral triangle whose area and perimeter are equal has an area (and perimeter) equal to \sqrt 432 .
433
433 is a prime number, a Markov number, and a star number.
434
434 = 2 × 7 × 31. It is a sphenic number, a nontotient and the sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83). It is the maximal number of pieces that can be obtained by cutting an annulus with 28 cuts.
435
435 = 3 × 5 × 29. It is a sphenic number, a hexagonal number, a self number, There are 435 compositions of 16 into distinct parts.
436
436 = 2 2 × 109. It is a nontotient, a noncototient, and a lazy caterer number.
437
437 = 19 × 23. It is a Blum integer.
438
438 = 2 × 3 × 73. It is a sphenic number and a Smith number.
439
439 is a prime number and a strictly non-palindromic number. It is the sum of three consecutive primes (139 + 149 + 151) and the sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
440
440 = 2 3 × 5 × 11. It is a Harshad number, an abundant number, a happy number, and the sum of the first 17 prime numbers. A440 (pitch standard) is widely used for the musical note A4, the A above Middle C, when tuning instruments.
441
441 = 3 2 × 7 2 = 21. It is a centered octagonal number, a refactorable number, and a Harshad number. 441 is also the sum of the cubes of the first 6 natural numbers: 441 = 1 3 + 2 3 + 3 3 + 4 3 + 5 3 + 6 3 .
442
442 = 2 × 13 × 17. It is a sphenic number and the sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
443
443 is a prime number, a Sophie Germain prime, a Chen prime, and an Eisenstein prime with no imaginary part. Mertens function of 443 is -9, a new low which stands until 659.
444
444 = 2 2 × 3 × 37. It is a refactorable number,
445
445 = 5 × 89. There are 445 series-reduced trees with 17 nodes.
446
446 = 2 × 223. It is a nontotient and a self number.
447
447 = 3 × 149. There are 447 1's in all partitions of 22 into odd parts.
448
448 = 2 6 × 7. It is an untouchable number, a refactorable number, and a Harshad number.
449
449 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (79 + 83 + 89 + 97 + 101). 449! is the largest factorial less than 10 1000 .
450
450 = 2 × 3 2 × 5 2 . It is a nontotient, a refactorable number, a Harshad number, and the sum of totient function for the first 38 integers.
451
451 = 11 × 41. It is a Wedderburn–Etherington number and a centered decagonal number. It is the smallest number whose reciprocal has period 10.
452
452 = 2 2 × 113. There are 452 surface-points of a tetrahedron with edge-length 15.
453
453 = 3 × 151. It is a Blum integer.
454
454 = 2 × 227. It is a nontotient and a Smith number.
455
455 = 5 × 7 × 13. It is a sphenic number and a tetrahedral number. The sum of the squares of the first 455 primes is divisible by 455.
456
456 = 2 3 × 3 × 19. It is a centered pentagonal number, an icosahedral number, the sum of a pair of twin primes (227 + 229), and the sum of four consecutive primes (107 + 109 + 113 + 127). It is one of the two values of the magical formula, IPSOS, the other being 696.
457
457 is a prime number, a self number, and the sum of three consecutive primes (149 + 151 + 157).
458
458 = 2 × 229. It is a nontotient. There are 458partitions of 24 into divisors of 24.
459
459 = 3 3 × 17. It is a triangular matchstick number.
460
460 = 2 2 × 5 × 23. It is a centered triangular number, a Harshad number, and the sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).
461
461 is a prime number, a Chen prime, a sexy prime with 467, an Eisenstein prime with no imaginary part, and a prime index prime.
462
462 = 2 × 3 × 7 × 11. Itis a pronic number, a sparsely totient number, an idoneal number, a stirling number of the second kind \left\ 9 \atop 7 \right\ , the binomial coefficient \tbinom 11 5 , and the sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89).
463
463 is a prime number, a centered heptagonal number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79). It is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503). It is a common baseball double play (see baseball positions). There are 463 days in the synodic period of Ceres.
464
464 = 2 4 × 29. It is a primitive abundant number. and the maximal number of pieces that can be obtained by cutting an annulus with 29 cuts. Since 464 = 21 2 + 21 + 2, it is the maximum number of regions into which 22 intersecting circles divide the plane.
465
465 = 3 × 5 × 31. It is a sphenic number, a member of the Padovan sequence, a Harshad number, and the 30th triangular number.
466
466 = 2 × 233. It is a noncototient and a lazy caterer number.
467
467 is a prime number, a safe prime, a sexy prime with 461, a Chen prime, and an Eisenstein prime with no imaginary part. : \sum_ n=0 ^ 10 467 ^ n is prime
468
468 = 2 2 × 3 2 × 13. It is a refactorable number, a self number, a Harshad number and the sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
469
469 = 7 × 67. It is a centered hexagonal number. 469! - 1 is prime.
470
470 = 2 × 5 × 47. It is a sphenic number, a nontotient, a noncototient, and a cake number.
471
471 = 3 × 157.It is the sum of three consecutive primes (151 + 157 + 163). It is a perfect totient number, additionally, φ(471) = φ(σ(471)).
472
472 = 2 3 × 59. It is a nontotient, an untouchable number,
473
473 = 11 × 43. It is a Blum integer and the sum of five consecutive primes (83 + 89 + 97 + 101 + 103).
474
474 = 2 × 3 × 79. It is a sphenic number, a nontotient, a noncototient, an untouchable number, the sum of the totient function for first 39 integers, and the sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
475
475 = 5 2 × 19. It is a 49-gonal number and a member of the Mian–Chowla sequence.
476
476 = 2 2 × 7 × 17. It is a Harshad number and an admirable number.
477
477 = 3 2 × 53. It is a pentagonal number.
478
478 = 2 × 239. It is a Companion Pell number. There are 478 partitions of 26 that do not contain 1 as a part.
479
479 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, a self number, and the sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
480
480 = 2 5 × 3 × 5. It is a highly totient number, the sum of a twin prime pair (239 + 241), and the sum of four consecutive primes (109 + 113 + 127 + 131). : \sum_ n=0 ^ 10 480 ^ n is prime
481
481 = 13 × 37. It is an octagonal number, a centered square number, and a Harshad number.
482
482 = 2 × 241. It is a nontotient and a noncototient. There are 482 series-reduced planted trees with 15 nodes.
483
483 = 3 × 7 × 23. It is a sphenic number and a Smith number.
484
484 = 2 2 × 11 2 = 22 2 . It is a palindromic square and a nontotient.
485
485 = 5 × 97. There are 485 triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions
486
486 = 2 × 3 5 . It is a Harshad number and a Perrin number.
487
It is a prime number, a Chen prime,
488
488 = 2 3 × 61. It is a nontotient and a refactorable number. φ(488) = φ(σ(488)),
489
489 = 3 × 163. It is an octahedral number.
490
490 = 2 × 5 × 7 2 . It is a noncototient, a self number, A (possibly arbitrary) large number in the Christian Gospel of Matthew. In Matthew 18:21–35, Jesus tells the Parable of the Unforgiving Servant, instructing Peter to forgive his brother "seventy times seven" times when his brother sins against him http://www.biblegateway.com/passage/?search=Matthew+18:21-35 .
491
491 is a prime number, an isolated prime, a Sophie Germain prime,
492
492 = 2 2 × 3 × 41. It is a refactorable number and the sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97). It forms a Ruth–Aaron pair with 493 under first definition.
493
493 = 17 × 29. It is the sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83). It forms 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 = \left\langle \!\! \left\langle 8 \atop 1 \right\rangle \!\! \right\rangle . It is a sphenic number and a nontotient.
497
497 = 7 × 71. It is a lazy caterer number and the sum of five consecutive primes (89 + 97 + 101 + 103 + 107).
498
498 = 2 × 3 × 83. It is a sphenic number, an untouchable number, and an abundant number
499
499 is a prime number, an isolated prime, and a Chen prime. 4 499 - 3 499 is prime.
References
* Delete: This could be a disambiguation page, the 420 for cannabis or the country code for telephone calls are valid searches, the rest is nothing any member of the general public would be using Wikipedia to look up. But this can just be deleted, it reads more as a page of trivia for math nerds than anything useful. Oaktree b (talk) 18:15, 4 July 2026 (UTC)