73 (number)

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73
Cardinal seventy-three
Ordinal 73rd
(seventy-third)
Factorization prime
Prime 21st
Divisors 1, 73
Roman numeral LXXIII
Binary 10010012
Octal 1118
Duodecimal 6112
Hexadecimal 4916

73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest integer with twelve letters in its spelled out name.

Contents

[edit] In mathematics

  • Seventy-three is the 21st prime number. The previous is seventy-one, with which it comprises the 8th twin prime. It is also a permutable prime with thirty-seven. 73 is a star number.
  • 73 is the largest minimal Primitive root in the first 100000 primes. In other words, if p is one of the first 100000 primes, then at least one of the primes 3, 5, 7, 11, 13, 17, ..., 73 is a primitive root modulo p.
  • 73 is the smallest prime congruent to 1 modulo 24.
  • The mirror of 73, the 21st prime number, 37, is the 12th prime number. The number 21 includes factors 7 and 3. Seventy-three in binary, 1001001, is a palindrome. In addition, of the 7 binary digits representing 73, there are 3 ones. Also, 37+12=49 (seven squared) and 73+21=94=47*2, 47+2 also being equal to seven squared. Additionally, both 73 and its mirror, 37, are sexy primes twice over, as 31, 43, 67 and 79 are all prime numbers.
  • The square root of 73 is 8.544. The sum of which (8+5+4+4) equals the product of 7 and 3; 21.
  • Every positive integer can be written as the sum of 73 or fewer sixth powers (see Waring's problem).
  • In base 5, the smallest prime with a composite sum of digits is 73.
  • 73 is the only prime repunit in base 8 (1118)
  • 73 is the smallest factor of the first composite generalized Fermat number in base 10 (104+1 = 10,001 = 73*137)

[edit] In science

In astronomy,

Messier object M73, a magnitude 9.0 apparent open cluster in the constellation Aquarius
The New General Catalogue object NGC 73, a barred spiral galaxy in the constellation Cetus
The Saros number of the solar eclipse series which began on 717 BC July and ended on 582 September. The duration of Saros series 73 was 1298.1 years, and it contained 73 solar eclipses.
The number of seconds it took for the OV-099 shuttle to explode after launch.
  • 73 is the length of the Arecibo message, sent to space in search for extraterrestrial intelligence.

[edit] In popular culture

Dr. Sheldon Cooper in The Big Bang Theory, played by actor Jim Parsons, said "The best number is 73. Why? 73 is the 21st prime number. Its mirror (37) is the 12th and its mirror (21) is the product of multiplying, 7 and 3. ... In binary, 73 is a palindrome, 1001001 which backwards is 1001001."

Sheldon's roommate, Leonard Hofstadter, then quips that "73 is the Chuck Norris of numbers," to which Sheldon replies "Chuck Norris wishes. [...] All Chuck Norris backwards gets you is Sirron Kcuhc!"[1]

Sheldon's devotion to the number is illustrated in several further episodes, when he wears a t-shirt emblazoned with it, for example in The Roommate Transmogrification.

[edit] In other fields

Seventy-three is also:

[edit] In sports

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