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.
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.
.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).
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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.
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 = 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).
432 = 24 × 33 = 42 × 33, the sum of four consecutive primes (103 + 107 + 109 + 113), 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 .
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
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 single by Buck 65, named after the baseball term
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
In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase.
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 = 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
^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.
^I. Nazar (1 April 2014). "The Hyper Text Coffee Pot Control Protocol for Tea Efflux Appliances (HTCPCP-TEA)". Ietf Request for Comments (RFC) Pages - Test (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.
^ abcd"Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
^"Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
^ ab"Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.