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87 (number)

From Wikipedia, the free encyclopedia
Natural number
← 8687 88 →
Cardinaleighty-seven
Ordinal87th
(eighty-seventh)
Factorization3 × 29
Divisors1, 3, 29, 87
Greek numeralΠΖ´
Roman numeralLXXXVII,lxxxvii
Binary10101112
Ternary100203
Senary2236
Octal1278
Duodecimal7312
Hexadecimal5716

87 (eighty-seven) is thenatural number following86 and preceding88.

In mathematics

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87 is:

  • the sum of the squares of the first four primes (87 = 22 + 32 + 52 + 72).
  • the sum of the sums of the divisors of the first 10positive integers.[1]
  • the thirtiethsemiprime,[2] and the twenty-sixth distinct semiprime[3] and the eighth of the form (3.q).
  • together with85 and86,[4] forms the last semiprime in the 2nd cluster of three consecutivesemiprimes; the first comprising33,34,35.
  • with analiquot sum of33; itself asemiprime, within analiquot sequence of five composite numbers (87,33,15,9,4,3,1,0) to the Prime in the3-aliquot tree.
  • 5! - 4! - 3! - 2! - 1! = 87
  • the last two decimal digits ofGraham's number.

In sports

[edit]
  • Cricket in Australia holds 87 as a superstitiously unlucky score and is referred to as "the devil's number". This originates from the fact that 87 is13 runs short of acentury. 187, 287, and so on are also considered unlucky but are not as common as 87 on its own.[5]

In culture

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  • TheGettysburg Address famously begins with the words "Four score and seven years ago...", or 87 years ago. The use ofscore to mean 20 is largely archaic, but the phrase "Four score and seven years ago" has become an idiom in its own right.[6]

In other fields

[edit]

Eighty-seven is also:

0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s

References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^"A001358 - OEIS".oeis.org. Retrieved2020-08-10.
  3. ^"A006881 - OEIS".oeis.org. Retrieved2020-08-10.
  4. ^Sloane, N. J. A. (ed.)."Sequence A056809".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Ferris, Sam (2014-11-02)."The real story behind Australia's unlucky number 87".cricket.com.au. Retrieved2022-01-27.
  6. ^"four score and seven years ago - Wiktionary, the free dictionary".Wiktionary. Retrieved2025-10-02.
  7. ^"Guide to model railroading scales and gauges".Model Railroader. 2 November 2011. Archived fromthe original on 22 June 2015. Retrieved2 October 2016.
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