73 (number)

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72 73 74
Cardinal seventy-three
Ordinal 73rd
Factorization prime
Prime 21st
Divisors 1, 73
Roman numeral LXXIII
Binary 10010012
Ternary 22013
Quaternary 10214
Quinary 2435
Senary 2016
Octal 1118
Duodecimal 6112
Hexadecimal 4916
Vigesimal 3D20
Base 36 2136

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.

In mathematics[edit]

  • 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.
  • 73 is an emirp, meaning that the reverse of 73, that is, 37, is also a prime number. Interestingly, 73 is also the 21st prime number while 37 is the 12th prime number.
  • The number 21 includes factors 7 and 3. The number 21 in binary is 10101 and Seventy-three in binary is 1001001. Both are palindromes. 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.
  • 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).

In science[edit]

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 Space Shuttle Challenger OV-099 shuttle to explode after launch.
  • 73 is the length of the Arecibo message, sent to space in search for extraterrestrial intelligence.

In other fields[edit]

73 is also:

In sports[edit]

  • In international curling competitions, each side is given 73 minutes to complete all of its throws.
  • In baseball, the single-season home run record set by Barry Bonds in 2001.
  • In basketball, the number of games the Philadelphia 76ers lost in the 1972–73 season (9–73), the most losses in NBA history.
  • NFL: New England Patriots John Hannah's retired #73
  • NFL: New York Jets Joe Klecko's retired #73
  • NFL: San Francisco 49'ers Leo Nomellini retired #73
  • NFL: In the 1940 NFL championship game, the Bears beat the Redskins 73–0, the largest score ever in an NFL game. (The Redskins won their previous regular season game, 7–3).
  • The rhythmic clapping at sporting events that precedes “Let’s Go!” is Morse code for “73”, an abbreviation meaning “best regards.” 73 was put at the end of 19th century telegraph conversations, as well as at the end of certain Ham radio exchanges. Clap-<pause>-clap-<pause>-clap-clap-clap<pause>clap clap clap <pause> equates to --- --- …(7) …--- ---(3).