400

[Calendar]  The years divisible by 400 are leap years, following the adoption of the current Gregorian calendar, created by Pope Gregory XIII in 1582 to reform the old Julian calendar.

 

[Calendar]  The last year of the 4th century.

 

[Game]  In the popular TV game show “Deal or No Deal”, a contestant has the choices of one of 26 suitcases of the prizes U.S. $0.01, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750, 1000, 5000, 10,000, 25,000, 50,000, 75,000, 100,000, 200,000, 300,000, 400,000, 500,000, 750,000 and the maximum amount is at least $1,000,000 (in a typical show).

  

[Math.]  400 = 202 = 70+71+72+73. 

The only other non-trivial case: 121 = 112 = 30+31+32+33+34.

 

[Math.]  A revolution, a full angle (or a full circle) is 360o = 2p radians = 400 grads (grades). (Units for angle measurements).

 

[Money]  In 1913, the CCH Standard Federal Tax Reporter, which spells out the U.S Tax code in all its riveting detail, was 400 pages long. In 2007, it is 67,204 pages.

 

[Movie]  Name of TV show/series/movie: “The 400 Blows”.

 

[Phone]  An NANPA/U.S. telephone area code reserves for service access.  (NANPA: North American Numbering Plan Administration).

 

[Sport]  The standard ranges of swimming/tracking competitions (meters): 50, 100, 200, 400, 800 and 1500. Also, for tracking: 2000, 3000, 5000 and 10000.

 

[Tech.]  The light sensitivity (speed) of most commercially popular camera films: ISO 100-200-400-800.

 

[World]  The ISO-3166 country code for Jordan.

 

401

[Calendar]  The first year of the 5th century.

 

[Math.]  A prime number.

 

[Money]  Plan 401(K), name of a popular retirement plan for U.S. private industries’ employees.

 

[Phone]  The only telephone area code for the state of Rhode Island, U.S.

 

402

 

403

[Math.]  162,409 = 169×961 = 4032 = 13×13×31×31.

 

[Math.]  Approximation:

e6 = 403.4287934… » p4 + p5 = 403.4287758…

 

404

[Math.]  The numbers 199989394, 199989404 and 199989464 begin with the digits 394, 404 and 464 respectively.

 

[Math.]   All 3 numbers 1,999,899, 1,999,900 and 1,999,901 have all their 404th, 414th, 424th, 434th, 444th and 454th powers starting with digits 404, 414, 424, 434, 444 and 454, respectively.

 

[Math.]  All numbers in the range [19,998,989-19,999,012] have all their 404th, 414th, 424th, 434th, 444th and 454th powers starting with digits 404, 414, 424, 434, 444 and 454, respectively.

 

[Tech.]  One of popular error message on the Internet: "404 File Not Found".

 

[World]  The ISO-3166 country code for Kenya.

 

405

 

406

[Math.]  A triangular number (sum of all integers from 1 to 28): 406 = 1+2+…+27+28.

 

[Phone]  The only telephone area code for the state of Montana, U.S.

 

407

[Math.]  One of only 4 numbers (other than 1), which are the sum of cubes of their digits: 407 = 43+03+73. The other such numbers, called Armstrong numbers, are: 153 = 13+53+33, 370 = 33+73+03 and 371 = 33+73+13. (Generalizable)

 

408

[Library]  ISBN-0-408 is the International Standard Book Number for books published by Buttherworths.

 

[Math.]  A well-know, even complicated, formula: arctan(1/239) = 4×arctan(1/5)–p/4 = arctan(1/70)–arctan(1/99) = arctan(1/408)+arctan(1/577).

 

[World]  The ISO-3166 country code for North Korea.

 

409

[Trivia]  Name of a commercial detergent/cleaning product.

 

400-409

[Library]  Numbers 400-499 are the first 3 digits in Dewey Decimal Classification System call numbers for library books in Languages and Linguistics. Numbers 400-409 are for general & dictionary works. 

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References [6]: Scientific American, I. Stewart, Mathematical Recreations, February 1997.